Price, who came in having faced the most shots by any goalie who has played three or fewer games, was rarely tested by a Buffalo team that was blanked by New Jersey on Wednesday night.
Montreal rebounded after blowing a two-goal lead Wednesday night at home in a 4-3 overtime loss to Tampa Bay.
Derek Roy scored and Ryan Miller made 26 saves for the Sabres, who have dropped four straight — all at home — since a season-opening win at Ottawa.
Before Roy's third-period goal, the Sabres hadn't scored since the third period of their loss Monday to Chicago, a streak of 118 minutes, 55 seconds.
After a scoreless first period, Picard gave the Canadiens a 1-0 lead with his first of the season 1:29 into the second. After his slap shot from the left point was blocked by Sabres forward Patrick Kaleta, Picard collected the puck in the lower left circle before sending a pass to the front of the net.
The puck ricocheted in off Buffalo defenseman Chris Butler's skate at the top of the crease.
Montreal grabbed a 2-0 lead with just 1:05 to go in the second when Gorges' one-timer from the right point beat Miller on the glove side.
The power-play goal was Montreal's first this season, snapping an 0-for-11 drought.
The Sabres cut the deficit in half when Roy scored his fifth of the season 3:36 into the third.
NOTES: The game was delayed for about 15 minutes as the Sabres recognized the 40-year anniversary of their first NHL home game with a pregame ceremony that included a re-enactment of the inaugural puck drop in 1970 that featured the Sabres' first captain, Floyd Smith. Former Canadiens captain Jean Beliveau, who was part of the original ceremonial puck drop, wasn't present. Former Canadiens great Henri Richard took Beliveau's place. ... Buffalo D Shaone Morrisonn missed his first game because of a groin injury sustained against New Jersey on Wednesday. Butler replaced him in the lineup. ... Buffalo lost seven straight home games to open the 1993-94 season. ... The Canadiens will play four of their next five at home, while the Sabres will play six of their next seven on the road.