Erik Karlsson had a goal and an assist and Leclaire stopped 29 shots for the Senators, coming off a 5-3 loss to the New York Rangers on Thursday night.
"Both teams are fighting hard for points right now," Leclaire said. "We're both not in a situation we expected to be in the standings so it was a pretty hard-fought game and it's good for us. Hopefully we can build some confidence out of it."
Brodeur made 26 saves in his first appearance in eight games following a right elbow injury as the Devils' losing streak stretched to four.
"It's more of the same for us," Brodeur said. "We could cry all about it all we want but we're the ones playing the game and we put ourselves in the situation that we need breaks all the time. If we played well right from the get-go it would have been a lot different."
The NHL's career victories and shutouts leader, Brodeur also drew his 35th career assist on Patrik Elias' power-play goal 4:46 into the second that tied it at 1.
Dainius Zubrus scored New Jersey's second power-play goal later in the second to draw the Devils within one. Ilya Kovalchuk assisted on both goals.
"It's not looking good," New Jersey center Jason Arnott said. "We're getting further and further away from that No. 8 spot [the last playoff spot]. It's getting near impossible. If we don't put a string of wins together here by Christmastime we're going to find ourselves going home early."
New Jersey had a possible tying goal by David Clarkson disallowed with 3:36 remaining in the third. The puck went in off Clarkson's left skate and referee Brad Watson immediately waved it off, a call that was upheld by a video review.
"They've got better cameras, I guess, than the one we saw and it must have looked like I kicked it," Clarkson said. "I can't really sit here and bash it, because I'm not that type of person, but I just thought that I shot the puck, it hit my skate and went right in the net, so it's a tough one to swallow, especially when that ties the game and we get the momentum back."
The Senators ended a two-game losing streak, winning for the fourth time in their last 14 games (4-9-1).
Michalek gave Ottawa its second one-goal lead 9:39 into the second. The Czech left wing backhanded a rebound past Brodeur for his sixth goal to make it 2-1.
Ruutu increased it to 3-1 at 11:55 when he banked a shot from behind the goal line off Brodeur and into the net for his second goal of the season.
Karlsson, who assisted on Michalek's goal, opened the scoring with an unassisted goal 15:30 in. The Ottawa defenseman's drive from the right point found its way through traffic and into the right side of the net.
"As long as you get the puck on net and you have someone in front that doesn't stop the puck it's usually a goal if the goalie doesn't see it and it goes next to him," Karlsson said.
Elias tied it at 1 with a power-play goal 4:46 into the second on a shot that Leclaire would surely like to replay. Brodeur began the play by playing the puck to Kovalchuk, who fed a pass to Elias. The veteran left wing's long shot struck Leclaire and popped up before bouncing behind the Senators' goalie into the net.
Zubrus got his fourth goal at 14:10. Travis Zajac fed a pass to Zubrus, who one-timed a drive past Leclaire to cut the lead to one.
Kovalchuk got his second point of the game, only his 13th in 27 games, with an assist on the play.
Brodeur's assist was his first of the season, and his 36th regular-season point, including a goal. Tom Barrasso holds the NHL records for assists and points by a goalie with 48 assists, two more than Grant Fuhr. ... Devils D Anton Volchenkov was given a warm reception when clips of some of his biggest hits with Ottawa were played on the video board during the first period. The former Senators defenseman waved to the crowd of 16,471. ... Senators RW Ryan Shannon was left out of the lineup for a second straight night.