The Bangladesh pace sensation gave away just 9 runs for two wickets bowling 4 overs as Hyderabad restricted Punjab to a below par 143-6 at the Rajiv Gandhi International Stadium on Saturday night.
Skipper David Warner then struck a blazing 59 off 31 balls, his fourth half-century in five matches, before his team coasted to their third successive win with 13 balls to spare.
But Mustafizur's spells were the story of the match as he left the batsmen groping in the dark to return with the most economical spell of the season for the Man-of-the Match award.
Asked to bat first, Punjab had lost the wicket of opener Murali Vijay (2) early to Bhuvneshwar Kumar.
The batsman failed to score any run in the first nine balls from Mustafizur after he was introduced into the attack in the last over of the powerplay.
A direct throw from Shikhar Dhawan caught Vohra short of the crease as Mustafizur claimed his first maiden over of the tournament.
After Shaun Marsh (40) and David Miller (9) tried to provide impetus by scoring 24 runs in two overs, Moises Henriques struck twice in the 10th to put the brakes on the momentum.
He removed Miller for an edge behind to the wicketkeeper before Mustafizur ran in for spectacular diving catch at fine leg to remove the dangerous Glenn Maxwell (1).
Punjab looked good for a total around 170 when Marsh launched Deepak Hooda for a six, but Mustafizur came back in the attack and trapped the batsman in front in the 14th over.
With the batsmen poking around to reach for his cutters, Mustafizur occasionally unleashed pitch-perfect yorkers to keep them pinned back to their crease.
When he took out Nikhil Naik (22) in the final over, thanks to a fine running catch by Henriques at mid-on, the big screen flashed the words 'Magical Mustafizur'.
In reply, a 90-run opening stand by Warner and Shikhar Dhawan (45) helped Hyderabad keep the target well within sight despite losing some quick wickets.
Warner maintained his swashbuckling form to race to his half-century in just 23 balls before holing out to long-on.
Riding on the strong platform for the chase, the home team looked in complete control despite Dhawan falling to a topedge after Aditya Tare had run himself out for a duck.
Eoin Morgan added a handy 25 to help his team cross the line in 17.3 overs.
The win put Warner and his men on third in the table while Punjab suffered their fourth defeat to languish at the bottom.