Brodeur got his 47th win and tied Parent's record set in 1973-74 by making 22 saves in regulation and then stopping four of six attempts in a shootout that the Devils twice extended with goals by Jamie Langenbrunner and Sergei Brylin on the fourth and fifth rounds.
John Madden, who scored for the Devils in regulation, ended the shootout with a backhand past Ray Emery. The goal brought a wry smile to the face of Lamoriello, who was a lot more serious on Monday when he fired Claude Julien with three games remaining in the season and the Devils in first place in the Atlantic Division.
The win was the Devils third straight and fifth in six games. Coupled with Buffalo's 4-1 win over Pittsburgh, it gave New Jersey a three-point lead with two games to go.
Antoine Vermette and Mike Comrie scored in the shootout for Ottawa, which had a two-game winning streak snapped in losing for only the second time in seven games.
Madden and Daniel Alfredsson scored 21 seconds apart in the third period for the other goals.