In reply, Hyderabad rode on a fourth-wicket unbeaten stand of 75 between Aiden Markram (41) and Nicholas Pooran (35) to achieve the target with seven balls and seven wickets to spare.
Hyderabad were in trouble at 77 for three but Markram stood firm in Pooran's company and finished the game off with a six in his 27-ball knock.
Kane Williamson's Hyderabad have been unbeaten after their opening two losses and jumped to fourth in the 10-team IPL table led by Gujarat Titans.
Malik, 22, remained the hero after his dramatic last over of the Punjab innings when he took three wickets including two on successive balls to be on a hat-trick on the final delivery which resulted in a run-out.
He became the fourth bowler in IPL history after Irfan Pathan (India), Lasith Malinga (Sri Lanka) and Jaydev Unadkat (India) to not concede a single run in the 20th over.
It was also the first instance of four wickets falling in an over without any runs.
Livingstone remained the lone batting performer for Punjab as he put on 71 runs with Shahrukh Khan, who made 26, for the fifth wicket before Malik's last over assault.