Bishop made 25 saves, and Vladislav Namestnikov had two goals and an assist to help Tampa Bay complete a season series sweep against Montreal with a 5-3 win at Bell Centre.
The Lightning (47-23-7) went 5-0-0 this season against the Canadiens, who swept Tampa Bay in the first round the 2014 playofs. The Lightning are 8-0-1 against Montreal in the regular season since 2013-14.
"Now we have an 'X' next to our name, which is nice," said Bishop, who started all five games against the Canadiens. "Now we have to keep trying to climb and catch these guys."
Tampa Bay has 101 points, one behind Montreal (47-22-8) for first place in the Atlantic Division. Each team has five games remaining.
"It's highly doubtful we'll see each other in the first round," Lightning coach Jon Cooper said. "So for us to sit here and say, 'You know what? Did we exorcise some demons here from what happened last year?' Sure we did. But, we can't look at this and say, 'Oh gee, we beat Montreal, all's good.' It's just two more points we banked, we got into the playoffs. They're going to go their way, we're going to go our way, who knows maybe we'll meet down the road. Now that would be special, if we did meet down the road."
Lightning rookie Jonathan Drouin scored for the first time since Dec. 15 to end a 42-game goal drought. Nikita Kucherov scored the Lightning's third goal of the second period to make it 3-1. Tampa Bay defenseman Anton Stralman scored into an empty net with 57 seconds left in the third.
Bishop assisted on Tampa Bay's first two goals in the second. He is the first goalie with two assists in a game since last season, when Ryan Miller accomplished the feat in his last game with the Buffalo Sabres in a 3-2 win against the Carolina Hurricanes on Feb. 25, 2014.
"I'll take them," said Bishop, who started all five games against Montreal. "I'm not really looking for them, but whatever. If it helps the team, it helps the team."
Canadiens goalie Carey Price made 39 saves. He leads the NHL with 41 wins, a 1.91 goals-against-average, and .936 save percentage. Price is tied for the League lead with nine shutouts, but went 0-4-1 against Tampa Bay.
"It's always good when you can beat a good team like that," said Bishop, who missed the playoffs last year because of a dislocated elbow. "Obviously Price is arguably playing the best hockey right now, so whenever you can beat him five times that says a lot. Now we just need to have the effort we had (Monday) on a consistent basis."
P.K. Subban scored his 14th goal on a power play with 3:50 remaining in the third period to pull Montreal within one.
Canadiens forward Max Pacioretty scored his team-leading 37th goal, and defenseman Jeff Petry scored his first goal in 14 games since he was acquired by Montreal in a March 2 trade with the Edmonton Oilers.
The Lightning went 1-for-5 on the power play with 10 shots. Canadiens coach Michel Therrien was very disappointed about his team's lack of discipline.
"It took away all momentum that we needed to have," Therrien said. "When you're undisciplined, you don't deserve to win. And I believe our group of defensemen really had a hard time."
Tampa Bay defenseman Victor Hedman left the game after one 29-second shift in the first minute of the third period and did not return.
"He couldn't finish tonight," said Cooper, who had no update on Hedman's condition. "We like to use those football terms, so what's the word? Questionable. That's what I'm going with."
The Lightning lost defensemen Jason Garrison and Andrej Sustr, and center Tyler Johnson, each to an upper-body injury in Tampa Bay's 4-0 loss at the Detroit Red Wings on Saturday. Garrison is expected to miss 3-4 weeks, Sustr is out 1-2 weeks, and Johnson is day-to-day.
Lightning center Brian Boyle played most of the game Saturday as a defenseman, and did so again in the third period against Montreal.
"Adversity's probably an overused term, but to patch together the (defense) corps we did, and then to lose (Hedman) in the third and to put Boyle back down there, it's a tribute to those guys," Cooper said. "They stayed engaged, they had a will to win this hockey game. That's a really good hockey team over there. I know they pushed back in the third a little bit, but all 200 feet of the ice I thought we played extremely well. With a lot of regulars out of the lineup, I can't say enough about the effort those guys gave."
Bishop got his first assist with a long pass to Lightning captain Steven Stamkos to set up Namestnikov's first goal at 1:24 of the second.
"That's a play we've made all year so it was nice to see him get rewarded and us finish off the play," Stamkos said.
Pacioretty scored his third shorthanded goal at 4:24 to tie the game 1-1, but his goal was still being announced when Drouin gave the Lightning a 2-1 lead with his third goal 33 seconds later at 4:57.
Ondrej Palat cut off a Montreal clearing attempt to set up Tampa Bay's third goal at 18:07. He passed to Namestnikov, who set up Kucherov's one-timer for his 28th goal.
Petry scored 23 seconds into the third period to draw Montreal within 3-2.
Palat got his second assist of the game on Namestnikov's second goal, his ninth, at 6:21.