It is second win of the season for the Royals from five matches while KKR have managed to get just one win under their belt, thus far.
While Jos Buttler's direct hit ended Gill's knock with KKR scoring 25 runs in the powerplay, KKR kept losing wickets at regular intervals and got reduced to 61/4 at the halfway mark.
Punjab Kings captain KL Rahul scored an unbeaten 60 and veteran Chris Gayle remained not out on 43 for the victors.
Punjab has lost their last three games while defending champions Mumbai are also coming after a loss against Delhi Capitals.
Archer plays for Rajasthan Royals and was initially expected to miss the first half of the IPL due to the injury.
On a good batting surface, Royals managed a total which may be 25 runs short but credit for the decent score goes to a counter-attacking effort from all-rounder Shivam Dube.
Despite the loss, Andre Russell hit six maximums in a breathtaking 54 off 22 balls and shared 81 runs off 39 balls with Dinesh Karthik (40) to bring KKR back in the hunt.
Last week, Ben Stokes was ruled out of the remainder of the IPL due to a finger injury and he has been sidelined for up to three months.
Bravo, who scored 20 not out off 8 balls, smashed a huge six off the last ball of the innings from Mustafizur Rahman (1/37) to ensure the Super Kings got close to 190.
Mayank Agarwal had top-scored for Punjab with 69 off 36 balls while his opening partner and skipper KL Rahul made 61 off 51 balls, taking them to 195 for four.
For DC, Tom Curran and Chris Woakes got a look-in with Kagiso Rabada and Anrich Nortje still serving their quarantine.