Tilak Varma also chipped in with a crucial 17-ball 21.
With MI at 95 for 3 in 14.3 overs, DC skipper Rishabh Pant made a strategic blunder as he refused to go for DRS after David nicked the first ball of his innings but the onfield umpire didn't give him out.
It came back to haunt DC as David slammed fours and sixes at will to bring down the equation to 15 off 14 balls. Ramandeep then provided the finishing touch with a six-ball 13.
READ| IPL 2022: Virat Kohli, Faf du Plessis and all of RCB spotted cheering for MI, see viral pics
DC finished with 14 points to remain in the fifth spot, while RCB joined Gujarat Titans, Rajasthan Royals and Lucknow Super Giants in the playoffs with 16 points.
.@mipaltan end their #TATAIPL 2022 campaign on a winning note!
The @ImRo45-led unit beat #DC by 5 wickets & with it, @RCBTweets qualify for the Playoffs. #MIvDC
Scorecard https://t.co/sN8zo9RIV4 pic.twitter.com/kzO12DXq7w — IndianPremierLeague (@IPL) May 21, 2022
This, after MI skipper Rohit Sharma won the toss and chose to bowl first. His bowlers duly responded as they scalped three early wickets, but Rishabh Pant (39 off 33) and Rovman Powell (43 off 34) tried to counterattack MI.
Axar Patel played the finisher's role as his unbeaten 19-run knock helped DC to a total of 159/7 in 20 overs.
Mumbai chased down the required total with five balls to spare.
With inputs from PTI