"I've said it before and I'll say it again, when I'm sitting in my rocking chair looking back at my career, maybe I can look at those things, but right now, I still have the drive to keep going," Julien said. "So those numbers aren't quite as important to me right now."
[WATCH: All Senators vs. Canadiens highlights]
Jesperi Kotkaniemi, Shea Weber, Paul Byron and Jonathan Drouin scored in the third period for Montreal (17-11-5), which is 5-1-0 in its past six games, including three wins against the Senators in the past 12 days. Carey Price made 16 saves.
"Even after two periods, I thought we deserved a little bit better," Weber said. "We talked about coming out in the third and maybe a little bit more desperation and a little more determined."
Colin White and Mikkel Boedker scored, and Mike McKenna made 42 saves for Ottawa (14-16-4), which has lost five of its past seven games (2-4-1).
Video: OTT@MTL: Byron finishes off great passing play
"Obviously, score, shots (47-18) and all that wasn't on the right side, but we were in this game for the great majority of it," McKenna said.
Kotkaniemi tied it at 2-2 at 2:06 of the third period after his wrist shot from the high slot hit the right post and bounced off McKenna's back into the net.
Phillip Danault appeared to give the Canadiens a 3-2 lead at 3:25, but Canadiens forward Artturi Lehkonen, whose pass set up Danault, was called for embellishment after being hooked by Senators defenseman Thomas Chabot.
"It obviously [stunk] that it was disallowed, but at the same time, that building got pretty loud and I think we fed off that," Canadiens forward Brendan Gallagher said. "I think the energy in here, we respond the right way and when this crowd gets going, it's fun to play behind and that was a big part of it tonight."
Weber scored to make it 3-2 at 10:06 on a wrist shot from the left circle nine seconds after a power play ended.
Video: OTT@MTL: Drouin pots empty-net goal
"We were a little upset and we transferred that energy the right way actually," Weber said. "It was a good reaction. I think guys were really obviously upset and I thought we deserved a goal there, but we did the right things and we came back and played the right way after that."
Byron made it 4-2 at 13:37, and Drouin extended the lead to 5-2 with an empty-net goal at 17:31.
Matthew Peca scored for the second straight game to give Montreal a 1-0 lead at 3:39 of the first period.
White scored 20 seconds later to tie it 1-1 on a rebound in the crease. Julien challenged the play for goaltender interference, but the call was upheld after a video review.
Boedker gave the Senators a 2-1 lead at 9:11 of the second period on a shot from the slot.
"In the first period, we came out real good, a solid first period, and you could see it fade away slowly in the second period and you could see the energy go down," Senators coach Guy Boucher said. "And in the third period, we just didn't have enough to follow them, plain and simple.
"The circumstances were as bad as you can imagine. It was a long road trip, the last game, back-to-back, they're not on a back-to-back, so we would have needed a bigger lead going into the third period, but we didn't have it and we couldn't keep up with their speed by the third period."
Video: OTT@MTL: Boedker converts feed from Stone
They said it
"When you think after 40 (minutes), whether or not we were in control of the game, you still have the lead. And we let them come at us in waves and we didn't have a match for their energy and the amount of pucks they put on net, and it's a shame because [Mike McKenna] held the fort for as long as he could." -- Senators forward Bobby Ryan
"It helps. That definitely helped. They had a lot of energy that way. They're booing, obviously not towards us, but they're fired up and we're fired up, and I think it was just a good intensity and energy from everyone and found a way to get it done." -- Canadiens defenseman Shea Weber about the crowd's reaction after the disallowed goal
Need to know
Julien became the fifth active NHL coach with at least 600 wins, joining Ken Hitchcock (832, Edmonton Oilers), Barry Trotz (777, New York Islanders), Paul Maurice (669, Winnipeg Jets) and Babcock (666, Toronto Maple Leafs).
Senators: Host the Nashville Predators on Monday (7:30 p.m. ET; RDS2, TSN5, FS-TN, NHL.TV)
Canadiens: Host the Boston Bruins on Monday (7:30 p.m. ET; TSN2, RDS, NESN, NHL.TV)
Video: Claude Julien gets 600th career victory in 5-2 win