Batter Ashutosh Sharma produced a brilliant rearguard knock but the Kings still ran out of steam on Thursday.
Sharma scored 61 off 28 balls, including seven sixes, as he helped Punjab recover from 6-77 to mount a serious challenge before the hosts fell short.
Pacers Gerald Coetzee and Jasprit Bumrah bowled Mumbai to victory, sharing six wickets in eight overs.
Suryakumar Yadav had earlier scored 78 off 53 balls to help Mumbai post 7-192 off their 20 overs, with Punjab managing 183 in 19.1 overs, which represented a pretty good effort after being 5-49 at one stage.
Rohit Sharma scored a brisk 36 off 25 balls, including three sixes, for Mumbai, paving the way for Yadav, who hit seven fours and three sixes in his second half-century of the season.
Tilak Varma contributed 34 off 18 balls, but Mumbai lost a bit of steam thereafter until David hit his 14 off just seven balls, including a couple of fours and a six.
In reply, Punjab were off to a disastrous start as they had no response to the Mumbai pacers.
Prabhsimran Singh was caught behind for a first-ball duck off Coetzee and then Bumrah bowled Rilee Rossouw for another golden duck with a searing yorker.
Sam Curran (six), who had opened the innings, was caught behind off Bumrah two balls later in the second over.
It became 14-4 in 2.1 overs as Liam Livingstone mistimed a pull off Coetzee and was out caught for one.
Impact player Harpreet Singh scored 13 runs but the damage was nearly irreparable.
Shashank Singh though went about this task, scoring 41 off 25 balls, including three sixes.
His counter-attacking knock breathed new life into Punjab's late order, especially Sharma who took over the mantle once Bumrah dismissed Singh in the 13th over.
Coetzee finally got the key breakthrough in the 18th over, as Sharma was out caught in the deep.
But Mumbai were penalised for a slow over-rate, meaning there were only four fielders allowed outside the 30-yard-circle for the final two overs.
Punjab needed 23 runs off the final 12 balls, took 11 off the penultimate over, but ultimately ran out of steam — and wickets.
Mumbai moved up to seventh, with the Kings ninth in the table.
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