Batting first, the Super Kings amassed 196 for three thanks to some fast scoring from Michael Hussey (46), Murali Vijay (53), Suresh Raina (43) and MS Dhoni, the captain (41 not out).
The Royals then lost key wickets at regular intervals and despite a fighting 52 off 36 balls from Ajinkya Rahane, they were all out for 133, with Doug Bollinger's three for 22 complimenting Ravichandran Ashwin's two for 24.
And Shane Warne, the captain, offered no excuses for the defeat, saying: "All credit to Chennai, and Dhoni in the end.
"It had nothing to do with the wicket, we were chasing 20 too many and it got difficult," the leg-spinner said.
Having lost the toss, Chennai saw Vijay dropped on four but were given a steady start by Hussey and reached 47 in five overs.
The Australian's 30-ball innings ended when he was bowled just short of a half-century by Johan Botha, but Vijay kept the tempo up - reaching a 36-ball 50 with a six - in a 58-run stand with Raina.
Dhoni, whose runs came from just 19 balls, then smashed three fours and three sixes to help collect 60 in the last five overs, despite Raina's late departure after 27 balls and six fours. Rajasthan's attempts to build a foundation were hit hard by the exits of openers Rahul Dravid (20) and Shane Watson (11).
The total lumbered to 68 as Rahane kept his calm - after Ross Taylor (six) and Ashok Menaria (two) failed to deliver - to build a gutsy 35-run stand with Botha (14). But the run-rate pressure found Rahane caught at long on, ending all hopes of an unlikely win as Suresh Raina's figures of two for nought eventually wrapped up the Royals' weak chase.
Dhoni was relieved to win the game that saw his team move up to second place in the table.
"It's good to be in the reckoning for the play-offs without leaving it for too late," the wicketkeeper-batsman said before giving his batting line-up credit for the win.
"The batting was poor in the last game [in the 10-run defeat to Kolkata Knight Riders on Saturday], but the platform was good this time from Hussey and Vijay, and Raina capitalised," he said.
* Compiled by The National staff with agencies