Byron was the only player to score in the shootout. Pacioretty scored in regulation for Montreal in its first victory since Dec. 22. Nikita Kucherov scored for Tampa Bay.
Pacioretty opened the scoring at 20 seconds of the second period.
Mikhail Sergachev, traded by Montreal to Tampa Bay for Jonathan Drouin in June, sent a weak pass up the left boards that was picked off by Pacioretty. The Canadiens captain skated into the slot and beat Andrei Vasilevskiy up high to end a 13-game goal drought dating to Nov. 30.
''No one will really understand what it's like when you go from a stretch where you're not scoring, getting robbed the first shift one game, getting one taken back (for offside) the next game, feeling confident in your game but not producing,'' said Pacioretty, a five-time 30-goal man who has nine this season.
Vasilevskiy, coming off two straight shutouts, saw his shutout streak end at 184 minutes, 49 seconds.
Only 44 seconds after the Canadiens took the lead, Kucherov skated into the slot and wristed his 26th goal of the season through traffic to beat Carey Price.
''I'll be honest, when I saw it was going to a shootout, I thought this could be a long one,'' Tampa Bay coach John Cooper said. ''But Byron made a really nice shot.
''That would go in on pretty much anybody. But if I'm going to sit here and circle the best (goalies) in the league, I think we may have just watched two of them.''
The Lightning wasted a big chance 6:33 into the third when Karl Alzner mishandled the puck at the far blue line, but Kucherov's backhand on the ensuing breakaway went well over the crossbar.
''That was the most fun I've had playing hockey in a long time,'' Pacioretty said. ''Our line played great. Carey played great. Their goalie played great. You could feel the energy in the building. All things considered, fans were really having fun tonight and really enjoyed the effort in the game. We have to take that in and remember how it feels and play for them and ourselves.''
Lightning: At Ottawa On Saturday night.
Canadiens: Host Vancouver on Sunday night.
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