Cooley, a Pittsburgh native, tied it 3-3 by batting the puck out of the air with his backhand just before the clock expired.
His goal came just 24 seconds after Ben Kindel had given Pittsburgh a 3-2 lead, scoring with a backhand on a loose puck just outside the crease. The 19-year-old forward was making his return after experiencing a vasovagal syncope episode, which is a sudden drop in heart rate and blood pressure that reduces blood flow to the brain, shortly after the Penguins departed Salt Lake City International Airport on Oct. 20.
In the overtime period, Mikhail Sergachev won it with a wrist shot from the slot off the rebound of Barrett Hayton's shot at 3:27.
Sebastian Cossa made 31 saves for the Mammoth (9-5-0), who have alternated wins and losses in their past seven games (4-3-0).
Kindel also had an assist, Erik Karlsson and Rickard Rakell scored, and Evgeni Malkin had two assists for the Penguins (5-6-2), who had won two straight after losing their previous four. Arturs Silovs made 30 saves.
Cooley scored his first goal of the game to put Utah ahead 1-0 at 4:40 of the first period. After intercepting a pass from Karlsson, he skated through the high slot to the left face-off circle for a wrist shot.
Cooley then made it 2-0 at 14:11 with his sixth goal this season, splitting Karlsson and Pittsburgh defenseman Spencer Stastney, and racing to the net front for a wrist shot blocker side.
Karlsson cut it to 2-1 at 8:38 of the second period, stickhandling around Mammoth forward Nick Schmaltz for a wrist shot from the inner edge of the right circle.
Rakell tied it 2-2 with a short-handed goal at 10:59 of the third period, collecting the puck in the neutral zone after it got past Cooley at the point and scoring his third goal in four games on a wrist shot from the right circle.
