Jim Dowd scored a short-handed goal midway through the third period to lift the Devils to their franchise-record 49th victory of the season, surpassing the mark set in 1997-98 and 2000-01.
Brodeur stopped 34 shots, including a breakaway in the second, to shatter the 33-year-old record in the city where Parent led the Broad Street Bullies to two Stanley Cup championships.
BUFFALO, N.Y. - Thomas Vanek scored twice and Buffalo matched a franchise record by beating Boston for its 52nd victory.
Ales Kotalik and Derek Roy also scored to help the Sabres rally from a 2-0 first-period deficit in Buffalo's final home game of the season. Goalie Ryan Miller stopped 20 shots to earn his 39th victory and set the single-season team record.
The Sabres (52-21-7) matched their win total from last season and clinched the Eastern Conference's top seed heading into the playoffs next week.
NEW YORK - Jaromir Jagr reached the 30-goal mark for the 15th straight season and added an assist to carry New York back into the playoffs with a victory over Montreal.
Petr Prucha also scored for the Rangers, who have reached the postseason for the second straight year and will enter the Eastern Conference playoffs as the sixth or seventh seed.
UNIONDALE, N.Y. - Jason Blake, Arron Asham and Miroslav Satan scored in the third period to preserve New York's faint playoff hopes with a victory over Toronto.
The Islanders trail ninth-place Toronto by one point and eighth-place Montreal by two points.
The losses by Toronto and Montreal clinched a playoff spot for idle Tampa Bay.
OTTAWA - Maxime Talbot scored with 9.8 seconds remaining to lift Pittsburgh over Ottawa and preserve an opportunity to claim home-ice advantage in a first-round playoff series against the Senators.
Pittsburgh moved into a tie with Ottawa for fourth place in the Eastern Conference with 103 points.
CHICAGO - Patrick Sharp and Jason Williams scored in the shootout to lift Chicago over Detroit.
Chicago posted its fourth straight win, while the Red Wings, by earning a point for reaching overtime, clinched their sixth straight Central Division Title.
COLUMBUS, Ohio - Rick Nash scored 1:04 into overtime and Columbus rallied to beat Dallas and snap a four-game losing streak.
Stars rookie goalie Mike Smith had a shutout going until Manny Malhotra tied it with a slap shot from the left circle with 6:57 remaining in regulation.
ST. PAUL, Minn. - Niklas Backstrom shut out Edmonton for the second time in three days, Marian Gaborik scored his 30th goal and Minnesota preserved slim hopes of winning the Northwest Division title.
Backstrom got his fifth shutout of the season.
NASHVILLE - David Legwand scored two goals, Paul Kariya notched his 500th NHL assist and Nashville snapped a three-game skid.
Nashville set franchise records with its 50th victory and 108 points. Rookie Alexander Radulov and Peter Forsberg also had goals for Nashville.