The defending champions had looked out of contention last night in their qualifier match with the Royal Challengers Bangalore when they required 77 off the last six overs to win.
But big hitting from Raina (73 not out), MS Dhoni, the captain, (29) and Albie Morkel (28 not out) saw them home with three balls remaining.
Morkel hit the winning runs as he hoisted Daniel Vettori, the Bangalore skipper, for a six, but it was Raina, who stole the show as his four boundaries and six maximums had kept his side in the hunt during his unbroken 50 ball innings.
He said in his post-match interview: "I just played my game, and play the big ones when the ball was in the zone. I was just looking to play till the 20th over."
A delighted Dhoni said: "We kept believing that we could do it, but you can say I was not 100 per cent confident.
"We know as a team we have the firepower to chase anything.
"This was a good scenario where the set batsmen kept on going, and the others chipped around him."
Bangalore's innings had been led by an excellent knock of 70 from Virat Kohli, which came from 44 balls.
He had shone, after Chris Gayle, the powerful West Indian who is the top scorer in this year's IPL, had suffered a rare failure, trapped leg before wicket by Ravichandran Ashwin for just eight.
Chennai had got off to a terrible start in reply to Bangalore's total as they lost openers Michael Hussey (0) and Murali Vijay (7) both cheaply inside the first two overs.
But Raina consolidated the innings with Subramaniam Badrinath, before opening his shoulders in the latter stages of the innings, along with Dhoni and Morkel.
A disappointed Vettori said: "That innings from Suresh took it away.
"You can never think the game is in the bag with this size of boundaries. But we expect to bowl a little bit better than we did."
Thanks to the new rules brought in for this season by the IPL, Bangalore, who topped the IPL group standings, have a second chance to reach Saturday's final.