Rohit Sharma got off to a good start after surviving an LBW appeal against Harshal Patel by using the DRS.
Suryakumar Yadav scored his third consecutive half-century against PBKS, this one off 34 balls.
Sam Curran dismissed Rohit Sharma and marshalled his resources very well as PBKS clawed back through the middle overs.
Harshal Patel claimed 3 for 31 in his four overs.
Tilak Varma scored a useful 18-ball 34* as MI got to 192 - the highest total in Mullanpur this season.
Jasprit Bumrah struck twice in his first over to dismiss Rilee Rossouw and Sam Curran while Coetzee dismissed Prabhsimran and Livingstone to leave PBKS tottering at 14/4.
Shashank Singh and Ashutosh Sharma put PBKS back on track in the chase with a brisk stand.
Ashutosh Sharma struck seven sixes in a sensational knock of 61 off 28 balls.
MI came back in the final three overs even though PBKS needed only 25 off 18. The five-time champs won by 9 runs.