James Reimer, who made 10 saves, left 32 seconds into the second period with a lower-body injury. He was replaced by Roberto Luongo, who made 27 saves.
"It was a gutsy effort coming back again (after a 4-3 overtime win against the Colorado Avalanche on Monday), and when it's overtime and a shootout it's anybody's game," Panthers coach Bob Boughner said. "I can't say enough about the guys battling and competing and finding a way to get a point."
McGinn tied it 2-2 at 5:46 of the third period, redirecting Brouwer's shot at the right post. Barkov gave Florida a 3-2 lead at 8:15, converting on a 2-on-1 with Brouwer seven seconds after the Panthers killed a penalty.
"We were scrambling, trying to finish off the rest of that kill, and [Barkov] made a great play and we were able to go on a 2-on-1," Brouwer said. "We were in good position defensively, giving ourselves a chance to make a break."
Stepan put the Coyotes ahead 1-0 at 8:15 of the second period, but Hoffman tied it at 1-1 at 14:44 on a one-timer from the left circle.