The Canadiens ended a seven-game road trip with a 6-1 record and handed the Panthers their third consecutive loss.
Bergeron broke a 3-3 tie with a power-play goal 1:52 into the third and Pouliot scored on a tip-in less than 3 minutes later.
Radek Dvorak brought the Panthers within a goal on a wrist shot with 13:57 to play, but Jaroslav Halak was perfect the rest of the way while making 32 saves. Tomas Vokoun surrendered all five goals on 42 shots.
Montreal's Mike Cammalleri scored his 20th goal on the power play 3:18 into the second to create a 2-2 tie.
The only loss the Canadiens suffered on their long trip was a 4-2 setback to Ottawa on Monday.