Leg-spinner Rahul Chahar returned impressive figures of 2-14 from his four overs to restrict holders Chennai to 131-4, a total Mumbai surpassed with nine balls to spare in the first qualifier of the Twenty20 tournament.
Yadav top-scored with 71 not out off 54 deliveries to drive Mumbai's modest chase as the three-time IPL winners await the second finalist in the title clash on Sunday.
"Three days now in which we can switch off before the final. Much needed break," said an elated Mumbai skipper Rohit Sharma.
"I knew we have the bowlers to restrict them. Have the confidence in our batters as well. Was important to restrict them to as little as possible, because it can get tricky against their quality spinners."
The Mahendra Singh Dhoni-led Chennai, also three-time champions, still have a chance to qualify for the final when they play the winner of the eliminator in the second qualifier on Friday.
Chennai had their moments in the match after the bowlers removed Mumbai openers Sharma, for four, and Quinton de Kock, for eight, inside four overs.
South African leg-spinner Imran Tahir also struck twice in successive deliveries to dent Mumbai's chase in the 14th over, but Yadav kept his calm.
His 80-run third-wicket partnership with Ishan Kishan, who made 28, was key in Mumbai cruising to victory.
Mumbai put their opponents on the back foot from the very start as hosts Chennai slipped to 32-3 after electing to bat first.
The 19-year-old Chahar struck first with the big wicket of Faf du Plessis for six. India's Suresh Raina (five) and Shane Watson (10) of Australian soon joined Du Plessis in the dug out.
Ambati Rayudu, who made 42, and Dhoni, who scored 37, put on an unbeaten 66-run fifth-wicket stand to give the Chennai total some respect.
"Somebody has to lose, things really didn't go our way, especially batting," said Dhoni.
"These are the best batsmen we have got, it looks like we are batting well, but at times they pull off shots that shouldn't be played.
"Hopefully, we will do well in the next game."
Chahar stood out with his wrist spin as he got able support from fellow spinners Krunal Pandya and Jayant Yadav who picked up a wicket each.
In the next play-off of season 12, Delhi Capitals will take on Sunrisers Hyderabad in the eliminator on Wednesday.