The 30-year-old’s final figures – 3-25 from four overs – represent his best return in this year’s IPL and he was named player of the match.
He was hit for 0-76 in the Royals’ opening match, the worst figures in IPL history, and followed with 0-33 in a defeat by Kolkata Knight Riders.
But 1-13 from three overs against Chennai Super Kings, including a wicket maiden with the opening over, showed promise – and he backed up that success against Punjab, hitting 94mph at one stage.
“The beginning of the tournament, games like that happen,” Archer said. “Most importantly I am happy to contribute to a team win.
“You have to understand you will be lucky in some circumstances and other times a batter may get ahead of you. Everyone puts in the hard yards.
“Every day is not going to be a great day but with the good days you have to enjoy them.”
Archer was named the IPL’s Most Valuable Player in 2020 but that was before his series of back and elbow injuries which have dogged his recent career.
England still hope he could return to Test cricket this year, either against India this summer or in the Ashes against Australia over winter.
Archer’s burst pushed the Royals further into the ascendency after contributions of 67 from Yashasvi Jaiswal, 38 from Sanju Samson and 43 not out from Riyan Parag took them to 205-4.
The Kings slipped further to 42-4 in pursuit and although a partnership of 88 from 52 balls between Glenn Maxwell and Nehal Wadhera, who hit 62 from 41, brought them back into the game, they fell away after Maxwell was caught at long-off for 30 and finished on 155-9.
The win lifts Rajasthan to seventh, while the Kings are fourth following their first defeat of the season.