Archer struck a 15-ball 32 after being promoted to number seven in the batting order to lift Rajasthan to 205-8 from a precarious 119-5 at Mumbai's Wankhede Stadium.
He then turned up in his primary role as a fast bowler, taking 3-17 as Mumbai finished on 175-9 despite Suryakumar Yadav's 60.
Former champions Rajasthan, who have been driven by strong performances, including by their 15-year-old batting sensation Vaibhav Soorayavanshi, knocked Punjab Kings from fourth place to complete the playoff lineup with 16 points.
Punjab ended the league stage with 14 points and needed Rajasthan to lose the game to prolong their season. The result also ended Kolkata Knight Riders' slim chances.
Defending champions Royal Challengers Bengaluru, Gujarat Titans and Sunrisers Hyderabad had already booked their playoff spots.
Bengaluru will face Gujarat in the first qualifier on Tuesday, and the winner will reach the final to be played in Ahmedabad on May 31st.
Hyderabad and Rajasthan will clash in the eliminator on Wednesday, with the loser out of the tournament and the winner heading into the second qualifier.
Put in to bat first, Rajasthan lost their openers, Yashasvi Jaiswal, for 27, and teenage prodigy Sooryavanshi, for four, to England spinner Will Jacks and Indian seamer Deepak Chahar.
Wicketkeeper-batter Dhruv Jurel hit 38, and Sri Lanka's Dasun Shanaka struck 29 off 15 balls before Rajasthan were five down in the 13th over.
Archer walked in two places above his usual number nine, and counter-attacked with three sixes and a four.
He departed in the 18th over but inspired Ravindra Jadeja, who hit an 11-ball 19, and Nandre Burger, who struck 10 off three balls, to help Rajasthan plunder 73 runs from the last five overs.
An upbeat Archer then rattled Mumbai with the ball as he sent back Rohit Sharma, caught behind for a fourth-ball duck in the first over.
He bowled Naman Dhir for six and fellow quick Burger dismissed Ryan Rickelton for 12 as five-time champions Mumbai soon slipped to 38-4.
Suryakumar put on key stands, including a sixth-wicket partnership of 48 with skipper Hardik Pandya, who made 34, to keep Mumbai in the contest.
Archer broke the stand with the wicket of Pandya and Suryakumar's departure in the 18th over cleared Rajasthan's path to the playoffs.
