"Of course, we knew we were in a dogfight to make the playoffs and it was going to be tough, but we thought we had a chance," Sullivan said.
Two days after being eliminated from post-season contention, Sullivan had the best game since his return April 6, scoring a key goal and adding an assist to lead the Devils to a 3-2 victory over the Montreal Canadiens on Tuesday night.
"But that didn't mean we were going to die," Sullivan said of the Devils being knocked out of playoff contention with Sunday's loss to the rival New York Rangers. "Without a doubt, there's a lot of pride on this team. We want to win every game. We weren't going to just give up."
The Devils turned to two other all-time greats to lead the way against Montreal. Patrik Elias scored the 375th goal of his career and long-time teammate Martin Brodeur stopped 19 shots in goal for the 669th victory in his storied career, as the Devils played the role of spoiler with the Canadiens trying to win the Northeast Division title.
The win was the third in the last four games for the Devils (18-18-10), who had lost their previous 10 games prior to the latest streak, eliminating them from playoff contention for only the third time in the last 20 years.
The loss was the fifth in the last six games for the sputtering Canadiens (27-14-5), who are battling Boston for top spot in the Northeast. Both teams have 59 points, but the Bruins have a game in hand.
"We knew that they were struggling a little bit, so we wanted to keep them honest," said Brodeur, who won for the 44th time in his career against the team he rooted for as a youngster. "We played hard and with intensity."
Elias' goal came in the first period and gave the Devils an early 1-0 lead. Jacob Josefson scored his first goal of the season, also in the first, and Sullivan scored in the second, increasing the advantage to 3-0.
"That's the worst recipe to have to play these guys," Canadiens coach Michel Therrien said. "They don't give you a lot of shots and they don't give you a lot of opportunities to score. We were on our heels from the first period on."
Max Pacioretty and Lars Eller each scored goals in the second period for the Canadiens, who couldn't find the net for the tying goal.
"We gave up two power-play goals and that's not how we play," Therrien said. "We have to do a much better job on the penalty kill. We have to make the right decisions and we have to be smart."
The Devils scored the first goal of the game in the first period off a power play, when Rene Bourque was called for interference. Just 17 seconds after Bourque went to the box, the Devils went right to work, with Zidlicky passing to Travis Zajac, who found Elias skating alone on Canadiens goalie Carey Price and Elias fired a wrist shot past Price. It was the 14th goal of the season for Elias and the 375th of his NHL career, all with New Jersey.
The Devils then got an even-strength goal with just 2:24 left. Jacob Josefson scored his first goal of the season off a mad scramble in front, a play where Josefson remained persistent and poked it past Price. It was the first goal that Josefson scored since March 29, 2012.
"I can't really spend too much time thinking about that," said Josefson, who spent most of the season in Albany of the AHL. "But getting a goal makes you feel better about yourself and gives you confidence. It was a nice feeling to score again and help us win."
New Jersey held a 2-0 lead after one period. The Devils hold a 14-1-4 record in games this season where they score first.
New Jersey then increased the lead to 3-0 on another power-play opportunity. Sullivan scored on a deflection after Zidlicky fired the puck at net.
"It was a great pass by Zidlicky," Sullivan said. "I just put my stick down. He shot it to my stick and I was able to deflect it in."
Pacioretty sliced the lead to 3-1 with a power-play goal of his own just 1:30 after Sullivan scored. The goal, Pacioretty's 14th of the season, gave the Canadiens some life.
Eller then sliced the lead to a single goal in the closing seconds of the second period, when Alex Galchenyuk made a play behind the goal and pushed a backhand pass to Eller in front with just 14 seconds left in the period. Eller's seventh goal of the season made the score 3-2 heading into the final period.
But the third period was scoreless, giving the Devils the victory.
"We just wanted to keep the game simple," said Brodeur, who will not play in the Devils' last home game Thursday against Pittsburgh, turning the netminding duties over to Johan Hedberg.
NOTES: The Devils gave slumping sophomore centre Adam Henrique the night off. Henrique had scored just one goal in the last 14 games, so Devils coach Pete DeBoer thought it would be best to take "a night to just watch." ... The Devils also announced that defenceman and captain Bryce Salvador will not play in the final three games of the season due to an injured wrist. ... Brodeur thought about taking the night off, but wanted to play against the Canadiens. ... Elias, who will be an unrestricted free agent in the off-season, reflected before the game that these could be his last games with the Devils.