Montreal had the first six shots, including an in-close backhander by Daniel Briere and a shot from the left circle from Plekanec. Nate Thompson got Tampa Bay's first shot 11 minutes into to the game, a backhander stopped by Price.
The Canadiens outshot Tampa Bay 15-9 through two periods.
"That was a tough start for us," Cooper said. "Our timing was off, our passes were off. A good thing Bishop was on because that could have gotten ugly for us quickly."
Bishop had won his previous five starts, allowing six goals during the stretch.
The Lightning had nine of the 11 shots during the first 9 minutes of the third, and 14-6 overall edge in the period.
Price made a save midway through the third on Radko Gudas' backhander.
NOTES: St. Louis has 950 points, two behind Rick Tocchet for 89th on the NHL list. ... Montreal D Josh Gorges returned after missing a game because of a lower-body injury. ... Tampa Bay D Eric Brewer and D Sami Salo both sat out with upper-body injuries. ... Canadiens rookie LW Michael Bournival, pointless over his previous 13 games, didn't play. ... Plekanec has 420 points with Montreal, one away from tying Stephane Richer for 29th on the team list. ... Montreal LW Max Pacioretty left early to receive stitches for a cut in his mouth, but returned to finish the game.