OTTAWA -- The Montreal Canadiens were finally able to close out the Ottawa Senators on Sunday night at Canadian Tire Centre.

Backed by a 43-save performance from goalie Carey Price, the Canadiens defeated the Senators 2-0 to take the best-of-seven, first-round playoff series in six games.

The win sends the Canadians to the second round against the winner of the Detroit-Tampa, which the Red Wings currently lead 3-2 ahead of their Game 6 on Monday.

The Senators, who charged into the playoffs with a historical 23-4-4 run over the final two months, couldn't write another amazing comeback story after falling behind in the series 3-0.

Canadiens winger Brendan Gallagher scored his first goal of the playoffs in the opening period and it stood as the only goal until winger Max Pacioretty sent a shot down ice into an empty net with less than a second remaining.

Senators goalie Craig Anderson made 18 saves in the loss.

The Senators were awarded their fourth power of the game when Canadiens winger Jacob De La Rose was called for tripping center Jean-Gabriel Pageau with 3:14 left in the third. But Price held the fort with the most notable save off a one-timer from Senators center Kyle Turris.

Price made a great sprawling save off Senators center Mika Zibanejad with Anderson on the bench for an extra attacker.

The Senators wound up 0-for-4 on the power play, while Montreal was also unable to produce with its one man-advantage opportunity.

The Canadiens held the Senators to just one shot on goal in three power plays through the first 40 minutes.

Still, the Senators outshot the Canadiens 16-3 the scoreless second period.

The Senators were victimized by a quick whistle near the seven-minute mark of the second period, when Price never did have control of a shot by defenseman Mark Borowiecki and Pageau swooped the puck into the net.

The Canadiens took their first 1-0 lead of the series when Gallagher batted down a point shot by defenseman Greg Pateryn and quickly whipped a shot behind Anderson for the lone goal of the opening period at the 13:26 mark.

NOTES: In hopes of adding some offence, Canadiens RW P.A. Parenteau dressed for the first time since Game 1. ... To make room for Parenteau, Canadiens C Brian Flynn was scratched. Through five games, Flynn had three points to tie him for the team scoring lead. ... Senators C Jean-Gabriel Pageau had 14 blocked shots through the first five games, including one off the stick of Canadiens D P.K. Subban that sent him limping off the ice. While there was some question as to whether Pageau and Senators LW Clarke MacArthur (lower body) could go in Game 6, both suited up. ... As soon as he left the ice in the second period of Game 5, MacArthur said he received a text from Canadian singer-songwriter Tom Cochrane, who he got to know through charity golf tournaments. "You know we've got a good following (when that happens)," said MacArthur. "He's a big hockey fan so it's pretty cool."