Punjab needed 10 runs from the last over, and Hetmyer (27no off 10 balls) held his nerve against death-bowling specialist Arshdeep Singh on Saturday.
After two dot deliveries, Hetmyer hit six, two and six to help Rajasthan cross the finish line with just one ball left.
Rajasthan finished on 7-152, in reply to Punjab's 8-147, cementing top spot in the league with a third straight win. For the slumping Kings, though, it was a fourth loss in six games.
Put in to bat, Punjab missed Shikhar Dhawan, and English allrounder Sam Curran stepped in as skipper.
The hosts were pegged back regularly by losing wickets as Rajasthan's spinners squeezed the scoring rate.
Yuzvendra Chahal took 1-31 in four overs and Keshav Maharaj picked up 2-23. Maharaj dismissed Jonny Bairstow (15) and Curran (six) and helped to reduce Punjab to 4-52 in 9.3 overs.
Jitesh Sharma anchored Punjab with 29 off 24 balls, including two sixes, but it was impact player Ashutosh Sharma who gave Punjab 147 to defend by scoring 31 off 16 until he was dismissed by Trent Boult (1-22) off the final ball.
Tanush Kotian replaced Rajasthan opener Jos Buttler and combined for 56 runs with Yashasvi Jaiswal, who scored 39 off 28 balls with four fours.
As opposed to Rajasthan's spin, Punjab's pace did the heavy lifting and got the vital breakthroughs. Kagiso Rabada dismissed both Jaiswal and in-form skipper Sanju Samson for 18.
Liam Livingstone bowled Kotian as Rajasthan's chase got bogged down at 3-89 in the 14th over.
But at 5-115, Hetmyer and fellow West Indian batter Rovman Powell took charge. Powell's 11-off-five cameo gave Rajasthan the impetus that Hetmyer used to finish with a flourish of three sixes.
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