Yadav and Tare were unbeaten on 97 and 90 respectively as they guided Mumbai to a healthy 285 for three in their second innings after the bowlers, led by Balwinder Sandhu, did well to dismiss Madhya Pradesh for 227 in their first essay.
Mumbai are sitting pretty with a huge 429-run lead with two more days to go in the match.
Resuming the third day on 197 for five, Madhya Pradesh lost Naman Ojha, who was out early in the day without adding to his overnight score of 79.
Ankit Dane (44) also failed to last long with Mumbai's bowlers claiming the last five wickets for a mere 30 runs.
Medium pacer Sandhu starred with five wickets and was well supported by Abhishek Nayar (3/56).
Mumbai continued their domination, as they came up with another good performance with the bat in their second innings.
Shreyas Iyer continued his good form as he stroked an entertaining 58 off 46 balls before Yadav and Tare forged an unbeaten 190-run stand for the fourth wicket.
Yadav hit 18 fours and Tare 15 as the duo put their team in the driver's seat.
Brief scores: Mumbai 371 and 285/3 (Aditya Tare 90 not out, Suryakumar Yadav 97 not out, Shreyas Iyer 58) vs Madhya Pradesh 227 all out.
Saurashtra thrash Assam by 10 wickets, enter Ranji final
Vadodara: Left-arm pacer Jaydev Unadkat wreaked havoc with the ball as Saurashtra dished out a dominant performance to thrash Assam by 10 wickets and sail into the final of the Ranji Trophy.
Such was Saurashtra's dominance that they wrapped up the five-day match inside three days with Assam batsmen falling flat in front of the opposition bowling unit led by Unadkat, who returned with impressive match figures of 11 for 112 runs.
Unadkat, who picked up six wickets in Assam's first innings, followed it up with yet another stellar show scalping five more victims in the second essay by giving away just 45 runs.
Resuming on their overnight score of 254 for five Saurashtra added 99 more runs before being bowled out for 353 in their first innings in reply to Assam's 234.
Centurion Cheteshwar Pujara (126) managed to add just 10 runs to his overnight score while Chirag Jani made 43 and Deepak Punia was unbeaten on 42.
Unadkat did the damage with the ball along with his pacer partner Hardik Rathod's show as the hunted in pair to bundle out a sorry-looking Assam for just 139 runs in their second essay, thereby setting up an easy target of 21 runs for Saurashtra to seal the affair which they did with considerate ease.
Despite the loss, it was a creditable performance for Assam this season as the North Eastern side made it to the last four stage of Ranji Trophy for the first time in the history of the tournament.
Brief Scores:
Assam: 234 and 139 all out in 39.1 overs (Jamaluddin Syed Mohammad 39; Jaydev Unadkat 5/45).
Saurashtra: 254 and 24 for no loss in 3.1 overs.
Image: Suryakumar Yadav (top) and Jaydev Unadkat.
Ranji semis: Mumbai hold edge; Pujara slams ton
Ranji semis: Iyer, Tare steady Mumbai; Assam fightback on Day 1
Injured Dhawal to miss Mumbai's Ranji semi-final vs MP
Government's power scheme lights up 253 villages
Herwadkar's century lifts Mumbai on Day 1 of Ranji quarters