Mathews hit an unbeaten half-century and then took one wicket for 27 runs in four overs as Deccan Chargers were restricted to just 150 for seven in their 20 overs in reply to Kolkata's 161 for four.
Captain Adam Gilchrist had got the Chargers off to a flying start, blazing 54 from just 35 deliveries, inclusive of three boundaries and three sixes, but his dismissal saw the Hyderabad team lose their way in the middle overs, with six wickets falling for the addition of 43 runs.
Earlier, Mathews and Owais Shah hit unbeaten half centuries to help Knight Riders recover after a disastrous start and post a competitive total.
Mathews wielded his bat with authority as he smashed 65 from 46 deliveries, laced with five boundaries and four sixes. Shah showed good composure in a fine knock of 58 from 48 balls, hitting three boundaries and three sixes. The two batsmen brought Kolkata back from the dead in a stand of 130 runs in 90 deliveries for the fifth wicket.
The duo took charge in the final overs, smashing 104 runs from the last ten overs, as Kolkata recovered from 31 for four in the sixth over without losing another wicket.
Kolkata Knight Riders:
Earlier, Deccan Chargers got off to a dream start after electing to bowl, claiming two wickets in the opening over.
Manoj Tiwary hit a full delivery from Chaminda Vaas straight to Rohit Sharma at midwicket and was out for a first ball duck.
Three deliveries later, captain Sourav Ganguly also fell for a duck when he edged one to VVS Laxman at first slip. The Kolkata side were reduced to one for two after the first over.
RP Singh caused Kolkata further grief when he had Cheteshwar Pujara caught at mid-on trying to loft straight after scoring 10 from 16 deliveries.
In the next over, youngster Jaskaran Singh claimed his first wicket when Hodge smashed a short delivery straight to Herschelle Gibbs at point for 13.
Mathews was lucky to survive off the first delivery he faced. He went to pull a short delivery from Jaskaran but got a top edge that went over the wicketkeeper for a six.
Deccan Chargers piled on the pressure after those early wickets as Kolkata reached 57 for four after ten overs.
Mathews, after a cautious start, broke the shackles, hitting consecutive boundaries off Jaskaran in the 12th over.
Shah got his first six of the innings when he slog swept Symonds over midwicket in the 15th over. In the next over, Ojha dropped short twice and was punished for a boundary each by both the batsmen through the midwicket region.
Shah and Mathews had repaired the damage to some extent, adding 72 runs in 65 balls for the fifth wicket, to take the total to 103 for four after 16 overs.
Having repaired the damage with a steady partnership, Shah decided it was time to cut loose in the final overs. The England batsman top edged Vaas over square leg for a six, and crashed the next delivery through point for a boundary.
Mathews showed scant respect for his compatriot as he lofted him straight down the ground for the second six of the over that fetched 18 runs.
He completed his half-century in style, carting T Suman high into the stands at wide long-on. It took the young Sri Lankan just 38 deliveries to reach the landmark; he hit four boundaries and two sixes, and helped Kolkata rally after the early wickets.
RP Singh also took some punishment in the penultimate over when Mathews hit him for a six and boundary as the Deccan bowlers lost the plot in the final overs.
Shah brought up his fifty, his first in the IPL, from 43 deliveries with a single on the off-side against Jaskaran in the final over and then slammed the young pacer for a six over square leg.
The last five overs fetched 69 runs for Kolkata as they finished on 161 for four in their 20 overs.
Deccan Chargers:
Ishant was unlucky not to pick the wicket of Gilchrist in his first over as Brad Hodge dropped a tough catch, diving to his left. The Deccan captain rubbed salt into the bowler's wounds by slamming him for consecutive boundaries in that over.
In the next over, Gilchrist showed he had lost none of his skills when he flicked Charl Langeveldt over the leg side for the first six of the innings.
The Deccan openers went after Laxmi Ratan Shukla in his opening over as Gilchrist and VVS Laxman hit a straight six each to take the total to 56 after five overs.
It was Kartik who brought Kolkata some relief when he claimed the wicket of Laxman. The right-hander was caught by the bowler himself off a top edge as he attempted another big shot on the leg side after scoring 22 from 14 deliveries.
Gilchrist (41) got another lifeline when Langeveldt failed to hold on to a difficult running catch off Mathews in the ninth over. He made Kolkata pay, smashing Hodge for a huge six over extra cover to bring up his half-century from just 30 deliveries, in the tenth over.
Herschelle Gibbs helped himself to a couple of boundaries off Mathews in the 11th over to continue Deccan's charge with the bat.
However, Kolkata struck against the run of play with the big wicket of Gilchrist for 54. The Deccan captain, who hit three fours and three sixes in his 35-ball knock, hit part-timer Hodge straight to Manoj Tiwary on the square leg boundary.
In the next over, Gibbs threw his wicket away when he hit Charl Langeveldt straight to Mathews on the long-off boundary in the 13th over.
Wickets continued to tumble as Andrew Symonds also departed early. The right-hander made just five before he tried to hit Ishant across the line on the leg side and was caught off a top edge.
After 15 overs, Deccan were reduced to 122 for four after 15 overs, needing 40 from the last five overs.
Mathews then showed his magic with the ball as he came up with the vital wicket of Rohit Sharma. The Mumbai youngster, who scored 13, was foxed by the slow bouncer from Mathews and ended up scooping it to the mid-off fielder.
Deccan were reduced to 133 for five after 17 overs.
Debutant Anirudh Singh scored a quick 14 from as many deliveries before he caved in to the pressure and was caught and bowled by Shukla.
The match was heading for a thrilling finish as Deccan needed to score 21 from the last two overs with just four wickets in hand.
Langeveldt brought all his experience into play and bowled a superb penultimate over. The South African gave away four runs in his final over while claiming the wicket of Chaminda Vaas for a duck.
Ishant also held his nerve in the final over, giving away just five runs, as Deccan Chargers finished on 150 for seven in 20 overs and lost by 11 runs.
Deccan lost three wickets for 28 runs in the last five overs and frittered the good start they got courtesy Gilchrist's quickfire half-century.
Langeveldt was easily the best bowler, claiming two for 26 in four overs, while the other bowlers also contributed with a wicket each.
Kolkata showed great temperament as they kept fighting and staged comebacks in both innings after messing up at the start.