The Mumbai captain continued his good run of form with the bat, scoring 72 from 52 deliveries, inclusive of eight boundaries and a six, before being dismissed a few deliveries from the end.
Mumbai, who cruised to 184 for five in 19 overs in reply to Chennai's 180 for 2, soared to the top of the IPL standings with eight points from five matches.
Shikhar Dhawan had given them a flying start, smashing 56 from 34 balls, inclusive of five boundaries and three sixes.
Muralitharan took two for 32 in his four overs but Mumbai chased down the target quite easily with Tendulkar holding one end up.
Earlier, Suresh Raina and Subramaniam Badrinath hit unbeaten half-centuries to power Chennai Super Kings to a healthy total after they were put in to bat.
Raina slammed 83 from 52 balls, hitting seven boundaries and three sixes, while Badrinath made 55 from 45 balls (6 fours) as the duo were involved in an unbroken stand of 142 runs in 91 deliveries for the third wicket, the second highest partnership in the IPL.
Harbhajan was once again the best bowler for Mumbai, claiming one for 25 in four tight overs while Ryan McLaren took one for 23.
Chennai now have a lot of work to do after losing their last three matches; they have four points from six games.
Chennai Super Kings:
Matthew Hayden went after Zaheer Khan in the second over, hitting four boundaries in a row. The first four was a thick edge to thirdman, followed by two more over the off-side cordon, while the fourth narrowly missed the bowler before crashing into the long-off boundary.
Parthiv Patel flicked McLaren over midwicket for his first boundary as Chennai raced to 31 from three overs.
Hayden called for the mini Mongoose in the fourth over, but it did not last long; Harbhajan Singh trapped him leg before wicket with the quicker delivery. The bat failed to come down in time and Hayden was struck right in front of the stumps after scoring 20 from 12 balls.
Patel also didn't last long; he flicked a full toss from McLaren on to his pads before it went back into the stumps; he was dismissed for eight as Chennai were reduced to 38 for two after five overs.
Suresh Raina ensured Chennai didn't lose the momentum as he flicked a full delivery from Dwayne Bravo for a six over square leg. The left-hander followed that with a splendid cover drive for a boundary, piercing the gap to perfection and reducing the ring of fielders on the off-side to mere spectators.
Raina went after Bravo again, in his third over; he hit the medium pacer for a six over midwicket and a boundary through point to reach 44 from 25 balls and take Chennai to 85 for two after ten overs.
At the other end, S Badrinath was content to play second fiddle to Raina. He got his first boundary off the 13th ball he faced when he tried to pull Lasith Malinga but got an edge that went into the boundary behind the wickets, in the 11th over.
Having found his footing, Badrinath also looked to lift his scoring rate with boundaries in successive overs to move to 26 from as many deliveries.
Once again Harbhajan kept things tight from his end, taking one for 25 in four overs, as Chennai reached 126 for two after 15 overs.
With the final five overs to come, the Chennai batsmen then decided it was time to take the attack to the bowlers. Raina started the charge, pulling Zaheer for a boundary through midwicket and then despatching Malinga into the stands over midwicket for a six in the next over.
Badrinath also stepped on the accelerator with boundaries in back-to-back overs from Malinga and Bravo respectively. He then hit a full toss from Zaheer straight back over his head for a boundary to bring up his half-century from 41 deliveries, in the 19th over.
Malinga bowled a splendid last over, giving the batsmen nothing to swing at or get under, as he dished out six yorkers.
Raina finished unbeaten on a cracking innings of 83 from a mere 52 deliveries, having hit seven boundaries and three sixes. After a slow start, Badrinath lifted the tempo in the final overs to score 55 from 45 balls, the two batsmen having added 142 runs in 91 deliveries for the third wicket, the second highest partnership in the IPL so far.
Except for Harbhajan, who took one for 25, and McLaren's one for 23, the rest of the bowlers struggled to contain Raina and Badrinath.
Mumbai Indians:
Sachin Tendulkar got the innings going with a delightful boundary through the off-side in the first over bowled by Albie Morkel. Shikhar Dhawan repeated the shot in the next over from Lakshmipathy Balaji for another boundary through the same region.
Dhawan then lifted the tempo, carting Joginder Sharma for four boundaries through the midwicket region to take the total to 50 for no loss after five overs. The left-hander seemed to have found his range as he slammed Balaji for two sixes through the leg side in the next over as Mumbai took control.
Left-arm spinner Shadab Jakati's first delivery of the match was reverse swept for a boundary by Dhawan, while Tendulkar got another one courtesy a misfield.
Dhawan completed his half-century off just 31 balls in style; he charged down the wicket and despatched Jakati into the stands over midwicket for a big six, in the 9th over.
Jakati then brought Dhawan back to earth, having him caught him at midwicket as he miscued another attempted heave through the leg side. The left-hander smashed 56 from 34 balls, laced with five boundaries and three sixes, before he was dismissed in the ninth over after a 92-run opening stand with Tendulkar.
Muttiah Muralitharan then struck in his second over, trapping trapped Saurabh Tiwary leg before wicket for 2 as Mumbai were reduced to 98 for two at the halfway stage.
That wicket saw Chennai tighten the noose; just 12 runs came from three overs, Mumbai reaching 106 for two after 12, needing to score 75 from the last eight overs.
Tendulkar then broke the shackles as he danced down the wicket and lofted Muralitharan over long-on for his first six of the tournament, in the 13th over.
Joginder made up for his horrible first over by claiming the wicket of R Satish in his next over. Satish played all over a full delivery trying to hit on the leg side and was bowled for five.
Tendulkar completed his half-century from 39 deliveries with a single off Jakati in the 14th over. In the same over, Dhoni messed up an easy opportunity to stump Kieron Pollard (6) off Jakati as the West Indian danced down the wicket but both the batsman and wicketkeeper lost the ball.
Dhoni introduced Thissara Perera in the 16th over of the innings and Sri Lankan pacer's first over turned out to be a disaster for Chennai. The pacer was hit for four boundaries in that over, two each by Tendulkar and Pollard; he gifted away four full toss deliveries in that over.
It turned out to be the turning point in the contest as Mumbai hit 19 runs from that over to reach 152 for three after 16 overs, left with the easy task of scoring 29 from the last four.
Meanwhile, Pollard seemed in a hurry to finish off things. He lifted Muralitharan straight down the ground for his first six. However, the veteran off-spinner had his revenge off the very next delivery when Pollard dragged it back on to his stumps after scoring 20 from nine deliveries.
Tendulkar hit boundaries in successive overs from Morkel and Balaji as the bowlers once gifted him full toss deliveries. However, Balaji had the big wicket of Tendulkar, who was beaten by the slower delivery, top edged a slow bouncer and was caught by wicketkeeper Mahendra Singh Dhoni.
A tired-looking Tendulkar walked back after a fine innings of 72 from 52 deliveries, his highest score in Twenty20 cricket after having hit eight boundaries and a six.
But there was no late drama as Dwayne Bravo hit a straight six and pulled the next delivery for a boundary to give Mumbai a deserved five-wicket victory.
Mumbai cruised to 180 in 19 overs and won the match by five wickets with six deliveries to spare.
As Tendulkar himself admitted, it was a calculated approach from the Mumbai batsman after Dhawan's blaze at the start which enabled them pace their innings at will.
Muralitharan was once again the top bowler for Chennai with two for 32 from four overs. But it was Perera's single over, which went for 19 runs, that changed the course of the match and saw Mumbai cruise in the end.
Mumbai went back to the top of the standings with eight points from five matches, while Royal Challengers Bangalore are second with eight points from six games.