"That's not the way we wanted to do it," Gionta said. "We had a good two periods, then we sat back in the third and they got themselves back into it."
Tampa Bay, which opened the season 6-1, has since lost five in a row (0-4-1).
"In the third period, our character showed up, again," Tampa Bay coach Guy Boucher said. "We have to build on a positive. That's extremely positive."
After Subban scored on a blue line shot at 8:21 of the second, Moen made it 3-0 from the low slot with 1:06 to go in the period. Moen snapped his 21-game goal drought, dating to Dec. 31, 2011, against Florida.
Gionta put Montreal ahead 1-0 when he tipped a pass through the crease from Tomas Plekanec past Lindback during a 5-on-3 power play with 43 seconds left in the first.
Hedman received a roughing penalty that set up Tampa Bay's two-man disadvantage. The Lightning allowed one goal on seven short-handed situations.
"A lot of the penalties ... I won't say anything," Boucher said.
Tampa Bay went 1 for 5 on the power play.
The Canadiens had a couple of quality scoring chances early in the first. Lindback made a save on Colby Armstrong's backhander during a 2-on-1, and Andrei Markov hit the post with a drive.
Lindback also made a lunging blocker stop on Markov's rebound attempt.
Price stopped an in-close redirection by Vincent Lecavalier late in the first, and had a glove save on Stamkos' shot from the right circle during a second-period power play.
Tampa Bay LW Ryan Malone sat out his second straight game and could miss three to four weeks because of an undisclosed lower-body injury. ... It was Gionta's first goal in nine games. ... Lightning RW Richard Panik, recalled from Syracuse of the AHL on Monday, made his NHL debut. ... Armstrong has gone 24 games without scoring a goal. He assisted on Moen's goal for first point in 17 games.
Copyright by STATS LLC and The Associated Press
Arena: Amalie Arena Location: Tampa, Florida
Referees: Dave Jackson, Ian Walsh Linesmen: Jay Sharrers, Jonny Murray
Attendance: 19,204 (100.0% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Brian Gionta (3)
(Power Play) Assists: Tomas Plekanec, P.K. Subban
P.K. Subban (3)
Assist: Lars Eller
Travis Moen (1)
Assists: Lars Eller, Colby Armstrong
Victor Hedman (3)
Assists: Tom Pyatt, Benoit Pouliot
Victor Hedman (4)
Assists: Teddy Purcell, Sami Salo
Sami Salo (1)
(Power Play) Assists: Vincent Lecavalier, Martin St. Louis
No scoring this period
Shootout attempt by Victor Hedman saved by Carey Price
Shootout attempt by Alex Galchenyuk MISSES
Shootout attempt by Martin St. Louis saved by Carey Price
Shootout GOAL scored by David Desharnais on Anders Lindback
Shootout attempt by Steven Stamkos saved by Carey Price