Raina cracked 10 boundaries and five sixes for Chennai to total 164-5. Rajasthan struggled and was all out for 126 in 19.3 overs. Kamran Khan did not bat after he was injured while fielding.
Chennai´s second win replaced Rajasthan in fifth place on the table.
Man-of-the-match Raina said he hoped the win would bring Chennai´s campaign back on track.
"Its a good win for us. Everything is looking positive. If we maintain that form things are going to be positive for CSK."
Chennai had to overcome a bad start, losing openers Matthew Hayden for 1 and Parthiv Patel for 3 inside the first four overs. Both fell to offspinner Yusuf Pathan, who took 2-17 from three overs.
Raina resurrected the innings, putting on 71 off 43 balls for the fifth wicket with captain Mahendra Singh Dhoni, who finished unbeaten on 22. Raina was dismissed in the last over just two runs short of the tournament´s second century. He was caught by a running Graeme Smith in the deep off Munaf Patel.
Raina thought he got the hundred because of an error on the scoreboard.
"I only found out (about the error) when I reached the dressing room," he said. "Anyway, it´s OK now, we won the match, it doesn´t matter."
Rajasthan captain Shane Warne said his team´s bowling in the final overs let Chennai off the hook.
"All our plans had worked well up front," he said. "Having them at 104-5 we should have reduced them to around 135. Sloppy fielding in the last four overs and bad bowling cost us the match."
In chasing, Rajasthan was never allowed to settle. Chief destroyer Balaji used the bouncy pitch and made his slower ball work. The pace bowler removed Ravindra Jadeja for 37, the dangerous Yusuf Pathan for 20 at 86-4, Warne for 3 and Siddharth Trivedi for 2.
Balaji was well supported by fellow seamers Albie Morkel and Jacob Oram, who also claimed two wickets apiece.
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