With the game tied 1-1 late in the second period, Callahan appeared to score the go-ahead goal for Tampa Bay, which had dropped the first two games of their playoff series at home against Montreal. Instead, the goal was waved off for goaltender interference.
The Canadiens went on to score before the end of the period, and ultimately beat Tampa Bay 3-2 on Sunday at the Bell Centre to take a 3-0 series lead over the Bolts.
After Callahan's goal was disallowed at 16:09 of the second, the referees and linesmen conferred, but did not overturn the decision on the ice.
Lightning coach Jon Cooper was furious on the bench.
"I was (angry) then, and I'm (angry) now," said Cooper. "It's tough to walk in that locker-room and look those guys in the eye when clearly that was our best game of the series. They deserved a better fate tonight."
The play started when forward Alex Killorn drove hard to the net, stumbling over Carey Price as he tried to beat the Canadiens goaltender with a shot between the legs. Price made the save before Killorn tripped over his pads and landed in the back of the net.
P.K. Subban, who was in the crease batting the puck out of mid-air, prevented Killorn from leaving the goal area. As the Lightning forward finally walked out of the net, he nudged Price, forcing him out of position.
Seconds later, Callahan jammed the puck past Price, but his celebration was cut short by referee Francis Charron's whistle.
The goal would have given Tampa its first lead since the second period of Game 1.
"I was just trying to get out of the way," said Killorn. "It felt like a good scramble there for a little bit. It seemed like it was a little while after we made contact.
"The play was going along, and then the puck went in. It felt like there was a little time there."
Killorn thought that Price jumped onto him as he was trying to leave the crease, and not the other way around.
"It's discouraging, but you have to have a short memory in those periods. It's playoff hockey," said Killorn. "We understand there's a lot of pressure on these referees. Whether the call is right or wrong, we need to move on from that.
"He (Charron) told me he thought it was the right call. That's fine by me."
Price didn't exactly see it the same way.
"It was kind of a mad scramble," the Canadiens goaltender said. "Their guy was in the crease and I tripped over him. That's why I was out of the play."
Two minutes after the Callahan goal was disallowed, Brendan Gallagher gave the Canadiens the lead when his shot rang off the crossbar and beat Bolts netminder Anders Lindback for his second goal of the playoffs.
"There's a high when the puck goes in like that," said Tampa's captain Steven Stamkos of the disallowed goal. "When it gets called off, you lose focus for a little bit. That's tough. Especially in the playoffs, in a tight game like that.
"We thought it was a good goal."
Stamkos briefly left the game after defenceman Alexei Emelin inadvertently kneed him in the head after he was knocked down to the ice late in the second frame. The Lightning medial staff cleared him to play in the third.
After Tomas Plekanec made it 3-1 for Montreal mid-way through the final period, Stamkos assisted on Matthew Carle's goal from the point to reduce the deficit. But the comeback ended there.
"We deserved better tonight," said Stamkos. "We'll have to use that as motivation for next game."
Down 3-0 in the series, Tampa Bay is in real danger of a sweep. The next game goes Tuesday in Montreal.
Despite disagreeing with the call on the ice, Cooper thought his team reacted well after the disallowed goal.
"It's still a tie game," he said. "You have to turn the page. Stuff like that happens. There was plenty of time to come back in the game.
"Let's call a spade a spade: we only scored three goals … I mean, two," added Cooper, facetiously. "And they got three. We just fell short."
Notes: Lightning rookie Ondrej Palat scored his first of the playoffs on Sunday after missing Game 2 of the series with an upper-body injury. Palat, who led the Lightning in the regular season with 59 points, possibly re-aggravated the injury after colliding with P.K. Subban in the third period of Game 1. … Travis Moen is day-to-day (concussion). … The Canadiens are hoping to win a playoff series for the first time since 2010, when the Philadelphia Flyers eliminated them in the Eastern Conference finals.