Chasing a challenging 153 to win, Rajasthan were so close to win as they needed just 15 runs off the last two overs but Morne Morkel and Umesh Yadav snatched the win for Delhi out of the jaws of defeat by conceding just 13 runs.
Morkel conceded just three runs in the penultimate over and also dismissed Brad Hodge (22) to turn the tide in the favour of his side.
Rajasthan needed two runs off the final ball after Rahane smashed Yadav for a six and took two in the fourth and fifth balls. However Rahane missed the last ball and Owais Shah was run out while attempting a single.
The unpredictability of the Twenty20 format was on display at its best as Rajasthan were running away with an upset win after the openers—Rahane and his skipper Rahul Dravid (40) -- raised a 99-run stand for the first wicket.
Rahane and Hodge then added 42 for the second wicket but it turned out to be a case of close yet so far, for Rajasthan.
Delhi had put up a challenging 152 for six after Virender Sehwag smashed a 63 off 39 balls at the top and Yogesh Nagar (27 off 20) provided the fireworks in the end.
With his knock Sehwag became the only batsman in the history of IPL to score four consecutive half-centuries.
Rajasthan's bowling was tight and except the last over when they leaked 20 overs, they made the formidable Delhi batting line-up to work hard for runs.
It was a difficult wicket for stroke-making but Rahane and Dravid read the track well and responded to the challenge sensibly. They kept finding boundaries but never attempted shots which risked losing wicket.
However, despite all the hard work, victory slipped out of their hands as they finished 151 for three.