Brodeur made 31 saves, got a couple of big blocks from his defensemen and goals by Andy Greene and Brian Gionta in a 3-0 victory on Friday night.
Scott Gomez, who set up the first two goals, added an empty-netter as the Devils took a 3-2 lead in the entertaining first-round Eastern Conference series. Game 6 is Sunday afternoon in Tampa, Fla. A seventh game, if necessary, would be played in New Jersey on Tuesday night.
The game ended with two fights and Devils assistant coach John MacLean and Lightning coach John Tortorella screaming at each other from behind their respective benches.
After letting in some easy goals in the first four games, Brodeur looked like the goaltender who set a single-season record with 48 wins this season. He was sharp, in position and impregnable in posting his 22nd career playoff shutout.
And there were plenty of big saves as the Lightning limited New Jersey to a franchise- record playoff low 14 shots.
Brodeur made a nice pad save in close on a short-handed shot by Ryan Craig in the first period and he was really on top of his game in the second, when Tampa Bay held a 14-7 advantage in shots.
With the Devils clinging to a 1-0 lead on Greene's first playoff goal, Brodeur made consecutive stops in close on Andreas Karlsson and Tim Taylor before Devils defenseman Richard Matvichuk made a sliding block on Karlsson with the net open.
The 34-year-old Brodeur had the crowd chanting "Marty, Marty" late in the second period when he stopped a spinarama move in close by Lightning defenseman Dan Boyle, a point shot by Lecavalier, and then Martin St. Louis all alone in front with a poke-check the knocked the puck off his stick.
Less than a minute later, Brodeur stopped a rolling puck in the crease after it hit off Karlsson's leg.
By then, the Devils had a 2-0 lead, and they laid back in third period. The closest the Lightning came to a goal was when Lecavalier, who has five goals in the series, hit a post with less than five minutes to play.
Greene, a rookie who came up late in the year and had only one goal, gave New Jersey the lead midway in the first period with a shot from the left point through traffic in front of Lightning goaltender Johan Holmqvist. Mike Rupp set up the shot by carrying the puck around the net and sending it to Greene, who also made a big block that denied St. Louis a shot on a first-period break. His shot got past Holmqvist and went into the net off the skate of defenseman Shane O'Brien. Gionta scored halfway through the second period on a two-on-one break with Patrik Elias. Defenseman Brian Rafalski intercepted a pass at the Devils' blue line and snapped a pass to Gomez, who sent Gionta and Elias away. Holmqvist got a piece of the shot with his glove, but it trickled past him into the net.