Royals signed off from the Jaipur leg of their campaign with a seventh win in eight matches to cement their table-topping status.
The visitors chased down Pakistan 178 with 10 balls to spare.
Gujarat Titans all-round performance guide them to 3-wicket victory over Punjab Kings.
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Titans were bundled out for 89 following which Capitals finished the chase in 53 balls
Mumbai innings looked like it was going smoothly but some sensational defensive bowling helped CSK seal the game.
KKR registered their fourth win in five games as they chased down the target with ease
Despite an excellent 19th over from Curran and a good effort from Arshdeep, Hetmyer guided Royals home with an unbeaten ten-ball 27.
Delhi Capitals, on a run of four defeats in five before the game, ended Lucknow Super Giants stranglehold on 160-plus defences.
Shubman Gill set up the chase but it looked like Royals had wrested control, until Rahul Tewatia and Rashid Khan came together.
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