Montreal's interim head coach earned his first victory after the Canadiens beat the Ottawa Senators 6-2 on Tuesday night.
The victory snapped a five-game losing streak for Montreal, which has struggled since Cunneyworth took over on December 17.
"It was nice to get him that first win," said Michael Cammalleri, who scored the game-winning goal. "Hopefully it makes him feel a little better here, him and everybody else."
Lars Eller, Tomas Plekanec, Louis Leblanc, P.K. Subban and Erik Cole also scored for Montreal (14-16-7), which scored six goals for the first time this season.
Raphael Diaz added three assists while Carey Price stopped 33 shots.
The pressure surrounding Cunneyworth and the Canadiens has been intense since the coaching change, and the players were relieved after finally earning a win.
"He's been facing a lot of scrutiny lately and it's great to see the guys step up and get the win for him," said Subban. "I'm happy to see him get that win, it's well deserved."
Subban had been a healthy scratch the previous game and was happy to come back with a goal and an assist.
"Nobody likes to be a healthy scratch, but I'm just looking forward and I was happy to be able to contribute," said Subban. "I hope we've learned from the past couple of weeks that we have to bring it every night."
Cunneyworth admitted he was pleased with the win, but said he would have liked it to come a little earlier.
"A win is a win and hopefully it's the start of many more," said Cunneyworth, a former captain of the Senators. "We had a good team effort overall."
Zack Smith and Jason Spezza scored for the Senators (17-15-5). Craig Anderson was pulled after allowing four goals on seven shots and Alex Auld finished the night allowing two goals on 21 shots.
Things didn't get off to a great start for the Canadiens as Ottawa scored less than two minutes into the game when Smith beat Price high over the shoulder.
But Montreal quickly turned things around scoring three goals before the end of the first period and never looked back.
"They definitely made the most of their opportunities," said Ottawa captain Daniel Alfredsson. "They didn't have a lot of chances in the first and then they’re up 3-1. They just made the most of their chances. We created some chances, but not enough to make up for the goals we gave up."
Eller tied it 1-1 with a wrist shot from the top of the faceoff circle at the five-minute mark. Plekanec gave the Canadiens the lead as he deflected Diaz's shot from the point and just over
It only got worse for the Senators in the second as Leblanc's wrist shot completed a great two-on-one with Cammalleri early in the second, which marked the end of the night for Anderson.
Auld didn't fare much better as Subban made it 5-1 with his third of the season.
Spezza gave some life to the home team as he banged home a Milan Michalek rebound. Michalek was playing his first game after missing the last five with a concussion. Alfredsson picked up his 650th career assist on the goal.
Cole added a power-play goal late in the third to make it 6-2.
Notes: The Senators unveiled a new high definition scoreboard for the first time Tuesday night. ... The Senators were without D Chris Phillips (undisclosed, day-to-day), C Jesse Winchester (concussion, day-to-day), and C Peter Regin (shoulder, indefinitely). Montreal was without RW Brian Gionta (lower body, indefinitely), D Andrei Markov (knee, indefinitely), C Scott Gomez (groin, indefinitely), RW Ryan White (groin, indefinitely). D Chris Campoli and D Yannick Weber were a healthy scratch.