Calgary coach Ryan Huska said he knew his team had a chance after the first shift of the third period.
"Oftentimes in the third, if you start well and put some pressure on, it gives your bench a little bit of jump," Huska said. "That first shift (with Zary-Kadri-Martin Pospisil) was a good one and we just kind of built on it from there."
Nico Hischier had a goal and an assist and Jacob Markstrom made 23 saves for the Devils (37-27-6), who have lost two of their past three. The Devils are third in the Metropolitan Division, six points behind the Carolina Hurricanes for second.
Markstrom is 1-5-0 in six games since returning from a knee injury on March 2.
"The goalie has to make a save, that's part of the job, but we got to do a better job of protecting him," New Jersey coach Sheldon Keefe said. "[Markstrom] is still trying to find his game. I haven't seen progress (since his return from injury)."
Calgary scored four consecutive goals on 15 shots in the third period.
Zary began the comeback when he scored to make it 3-2 at 6:50 of the third period on a snap shot from the high slot.
Wolf then denied Dawson Mercer with his left pad on a short-handed breakaway at 7:51 of the third to keep Calgary within one goal.
"I felt like they were trying to make me make the move first, which I kind of did but was able to recover," Wolf said. "They've got some high-end skill over there and I'm just glad we were able to find one more than them."
Miromanov tied the game 3-3 at 15:40 on a snap shot low in the right face-off circle.
"I saw an opportunity to go far side there," Miromanov said. "'Markie' was here when I got traded so it's always nice when you have a goalie on your team, but then the goalie goes to the other team and you kind of know the holes to put it in. It's a big goal to tie the game and the guys took off from there."