Bangalore will face Lucknow Super Giants in Wednesday's eliminator game, while Gujarat Titans will take on Rajasthan Royals in Tuesday's playoff match.
Delhi had their qualification fate in their hands, but they were knocked out by Mumbai as Jasprit Bumrah's three-wicket haul and Tim David's quickfire 34 off 11 balls proved vital.
Delhi set Mumbai a target of 160 and they looked to be on course for a win, with Mumbai 92 for 2 at the end of 14 overs, requiring a whopping 68 runs in six overs.
In the 15th over, Delhi appealed for a caught-behind for Mumbai batsman David but the umpire turned it down.
Delhi captain and wicketkeeper Rishabh Pant opted against a review and was left to rue his decision after replays showed David feathered an edge off Shardul Thakur and would have been out for a duck.
Gifted a lifeline, David went on to hit four sixes and two boundaries as he led Mumbai to a win, crushing Delhi's hopes of advancing.