MONTREAL - Lightning coach Jon Cooper wouldn't let his team go down without a fight.

Trailing 3-1 after 40 minutes in Game 4 and staring elimination in the face, Tampa Bay made a game of it late as it scored twice in the third period to put the Canadiens on their heels.

Montreal's Max Pacioretty, however, scored with less than a minute to play in the third on Tuesday night to lead the Habs to a 4-3 victory and complete a four-game sweep of the Lightning.

"The big thing was, if we were going to go down, we were going to go down swinging," said Cooper. "And I thought we went down swinging."

With everything going Montreal's way for the first two periods, Tampa's Victor Hedman scored at 3:29 of the third to reduce the deficit, banking the puck off Carey Price's pad from behind Montreal's net.

Tyler Johnson scored the equalizer three minutes later with his first of the playoffs. Johnson found himself all alone in front of Price after the puck took a fortunate bounce off of Tomas Plekanec's skate in front of the goal.

"There were 21,000 people who were a little nervous in that third period," said Cooper of Tampa storming back, quieting the Bell Centre crowd in the process.

The crowd's nerves were settled when Pacioretty put home a rebound between rookie goaltender Kristers Gudlevskis' legs with 43 seconds remaining in the game.

While Cooper would have much preferred extending the series, he was proud of his young Lightning team??? which included 11 players that had never made it to the post-season.

"Ultimately, our goal was to make the playoffs. We did that," he said.

Cooper, a native of Prince George, B.C., spent three seasons coaching Tampa Bay's former and current American Hockey League affiliates, the Norfolk Admirals and Syracuse Crunch, before joining the Lightning in 2013. He compiled a 133-62-26 (.661) record in 221 AHL games and won the 2012 Calder Cup with the Admirals.

Cooper joined the Lightning at the end of last season, replacing Guy Boucher with 16 games remaining in the calendar. He led the team to a 5-8-3 record, but failed to make the playoffs. The Lightning finished 14th in the Eastern Conference, 15 points out of playoff contention.

Things were different this campaign. With Cooper at the helm for his first full season, the Lightning scored 240 goals and finished with 101 points??? one point ahead of Montreal in the standings. That extra point gave Tampa home-ice advantage in the playoffs.

"We had a hell of a year," said Cooper, who's a potential Jack Adams Award candidate for coach of the year. "To get north of a hundred points is an outstanding accomplishment for the lineup that we put on the ice night after night, with a bunch of guys who had never played in the league before."

But the impressive point total and home-ice advantage would mean little in the end. The Canadiens took both games on the road, winning 5-4 and 4-1 at the Tampa Bay Times Forum last week, before winning consecutive home games to complete the sweep.

"We wanted to make sure that Tampa Bay Lightning fans, wherever they were, were proud of their team," said Cooper. "They made me a better person, a better coach. I couldn't have been more proud to coach that team.

"I don't want there to be a sour taste because we didn't win a game in the playoffs."

Cooper is hopeful the post-season series, no matter how short, will prepare his young team for next year.

"You need to be in these positions and feel the atmosphere to understand the magnitude," said Cooper. "Until you're in it, you really don't understand what it's all about."

"Cooper's a good coach," said Lightning captain Steve Stamkos. "He has the respect from all the players. He came up with a lot of the young guys on this team. So the transition for them was a lot easier, being comfortable and confident. We relied heavily on those young guys."

Notes: Quebec singer Ginette Reno sang the Canadian national anthem. ??? Lightning defenceman Radko Gudas missed the game with a lower-body injury. ??? The Canadiens won a playoff series for the first time since 2010. ??? The series sweep was Montreal's first since 1993, when they beat the Buffalo Sabres in the division final en route to winning the Stanley Cup. ??? The Habs have now swept 22 of 31 playoff series after taking a 3-0 lead.