The Australian quick saw one of his overs disappear for 22, but his other three went for 15 accompanied by the crucial wickets of Ryan Rickleton and Hardik Pandya.
That was enough to carry Royal Challengers Bengaluru over the line against Mumbai Indians, their first win at the Wankhede since 2015, edging the clash by 12 runs after posting a daunting 5-221.
The match was notable for the return of Jasprit Bumrah, playing his first match since back trouble curtailed his involvement in the Sydney Test in early January. Looking as sharp as ever he produced the most economical bowling of the match, conceding 29 off his four overs.
But while Bumrah restrained RCB he could not dismiss them. Virat Kohli (67 off 42 balls) and Rajat Patidar (64 off 32) provided the core of an innings given late impetus by a 19-ball 40 not out from Jitesh Sharma.
Chasing 11-an-over the home team needed a fast start, and at 1-34 of three overs they were on course. Then Hazlewood entered the attack.
His third ball was cracked for four by Rickleton, but his fourth thudded into the South African's pads. Not out said the umpire, believing it pitched outside leg with Hazlewood bowling over the wicket to the left-hander. RCB went upstairs, DRS showed the ball pitched in line, and Rickleton was on his way.
Hazlewood then bowled six successive dot balls to superstar bat Surykumar Yadav, before stepping out of the attack with 1-6 from his two overs and Indians well behind the rate at 2-54 off six.
When the big Australian returned Mumbai were 4-116 off 13 with Hardik Pandya fresh at the crease. This time Pandya hit his first three balls 6-4-6 then, after a wide, another four. Hazlewood was now 1-28 off three overs.
It wasn't personal. Next over Hardik hit elder brother Krunal Pandya for successive sixes.
The assault brought Mumbai back into the game but even with Hardik and Tilak Verma adding 89 off 34 balls the rate was still above two-a-ball when the latter fell for a 29-ball 56.
Back came Hazlewood and Hardik again launched into him, but this time it did not carry and Liam Livingstone ended the Mumbai captain's innings on 42 off 15 balls.
Hazlewood completed his stint with 2-37 off four overs, handing the last over to Krunal with 19 required.
Now the other Australian, Tim David, joined the party. Having faced one ball, from which he scored a single, he had spent the match watching from the boundary, either in the dugout or guarding the perimeter. Which he where he was, at long off, to nonchalantly catch a drilled Mitchell Santner drive.
Next ball he took another catch, though the credit lay with Phil Salt who did the first half of an extraordinary relay catch, leaping to pluck Deepak Chandar's slog and lobbing it to David while in mid-air.
There was time for Krunal to take another wicket to finish with 4-45, and Pandya family bragging rights. "We both wanted to win but only one of us could," said Krunal, adding of Hardik: "He batted well, I feel for him."
