McCullum looked dehydrated in humid conditions in Chennai but still managed to smash seven fours and four sixes in his 61-ball knock, to help the Super Kings set 158.
Shane Watson ??? who fell to a sensational catch by Dwayne Bravo on the boundary ??? top-scored with just 28 in a disappointing effort with the bat from the Royals.
Ravi Jadeja took 4-11 to help reduce Rajasthan to 145-9 in reply and send Chennai back to the top of the IPL table.
On a tricky two-paced wicket, Chennai initially struggled to 15-2 in the fourth over, despite having won the toss and chosen to bat.
Dwayne Smith was the first to fall for six, caught at mid-on by James Faulkner off Ankit Sharma (1-31), soon followed an over later by Suresh Raina to the same fielder but at mid-off.
That was the first of three wickets for the impressive Chris Morris (3-19) but Rajasthan had to wait for 13 overs until they grabbed their next wicket, as McCullum and Faf du Plessis (29) put on 101 runs together.
Du Plessiss was the first to fall ??? run out ??? before an exhausted-looking McCullum followed an over later, top-edging an attempted pull off Morris to reduce Chennai to 129-4.
Morris struck again the very next ball as Pawan Negi slapped him straight to cover and he was on a hat-trick. It didn???t come though as Bravo safely saw it out.
Bravo (15 off eight balls) and MS Dhoni (13 off seven) then added a couple of lusty blows late on to take Chennai through to 157-5 from their 20 overs.
Ajinkya Rahane ??? leading run-scorer in the 2015 IPL ??? and Watson, who have so often got the Royals off to a good start, set a solid platform.
They hit 37 inside the first six overs before Rahane (23) fell to Mohit Sharma, caught by Bravo ??? his first but slightly less spectacular catch of the innings.
Steven Smith then became Jadeja???s first victim, bowled round his legs for four.
Watson attempted to rebuild the run-chase but when he departed, looking to hit Jadeja straight down the ground for six only to be caught by Bravo brilliantly on the boundary, the Royals fell apart.
Jadeja added the scalps of Karun Nair (10) and Deepak Hooda (15), to reduce the Royals to 90-5, before it was the Bravo show late on.
He first dropped a sitter off his own bowling ??? a top edge from Sanju Samson (26), but accounted for the wicketkeeper-batsman soon after.
Another terrific catch ??? at cover this time ??? got rid of James Faulkner (16), before Bravo???s second strike with the ball, dismissed Ankit in the final over.
It puts Bravo top of the wicket-taking table in the IPL, with the 12-run win also sending Chennai top.