Heatley, the Senators' two-time 50-goal scorer, took a shot from the right boards that struck Brodeur's right skate and went between the goalie's pads late in the second period to give Ottawa a 2-1 edge.
"Honestly, that one I was trying to hit [Jason] Spezza off the backpost and got a good bounce," Heatley said. "But it's definitely been part of our game plan to get pucks to the net whenever we can."
Brodeur clearly hadn't expected the sharp-angled shot and said he didn't see it.
"I saw him going up the boards with it and I looked in front and the puck was through me already," Brodeur said.
Ottawa moved within one win of reaching the Eastern Conference finals for the second time. Game 5 is Saturday night in New Jersey.
The Senators, who have made 10 straight playoff appearances, lost the 2003 conference finals in seven games to New Jersey, which went on to win its third Stanley Cup over Anaheim.
Heatley also helped Alfredsson open the scoring 4:34 in with a centering pass from behind the net.
"We seem to be comfortable playing with the lead," Fisher said. "I think we've learned throughout the season. We get up and then teams seem to come back, and we'll take the momentum back. We seem to be doing the right things right now. The guys are playing pretty well defensively and Ray's obviously making timely saves, and that's a big part of it."
Jay Pandolfo tipped Paul Martin's point shot past Emery midway into the third period to draw New Jersey within one. Brian Gionta had tied it 1-1 on a power play in the second period with his eighth goal of the playoffs.
Gionta's goal ended a 153:33 home shutout streak by Emery, who made 25 saves for his second playoff shutout in Monday's 2-0 win.
"We were able to get a little bit more at them than we did on Monday," Martin said. "It's tough. You can tell that they played well, but we didn't capitalize on some of our chances."
Brodeur, who made 33 saves, has lost three of four in the series despite stopping 130-of-141 shots, a .922 save percentage.
"I got a lot of work," Brodeur said. "I got a lot of shots against again, so it's just unfortunate that we couldn't get the win."
The Devils have faced a 3-1 deficit six times previously and came back to win one series, when they beat Philadelphia in the 2000 Eastern Conference finals.
"You can't win three in one game, so we'll look at one game at a time here," Devils defenseman Colin White said.
Heatley, who assisted on Spezza's empty-net goal Monday, extended his points streak to five games when he set up Alfredsson's fifth goal of the playoffs.
Alfredsson set the scoring play in motion when he took Spezza's pass and shot the puck along the right boards. The Senators captain cut straight across to the goalmouth to take Heatley's centering pass from behind the net before beating Brodeur with a shot to the top right corner.
Gionta tied it when he put Patrik Elias' rebound past Emery for his seventh goal in seven games.
Heatley summoned a roaring cheer from the Scotiabank Place record crowd of 20,248 with 5:16 left in the second period when his shot along the ice from the right corner struck Brodeur's right skate and slid between his pads and into the net.
Fisher made it a two-goal lead when he drove into the Devils' zone and beat Brodeur with a 40-foot wrist shot.
"I just tried to get a quick shot off and whenever you beat him from there it's obviously a pretty good feeling, especially in the third period of a game like that," Fisher said.
Pandolfo cut the lead to one midway through the period when his deflection beat Emery for a goal that stood up to a video review.
Elias put a couple shots toward the net in the final minute with Brodeur pulled for an extra attacker, with one stopped by Emery and a second blocked by defenseman Anton Volchenkov.
"We pushed hard and gave everything we could," Elias said. "Even when we pulled the goalie we had a couple of good chances."
Brodeur got his eighth career playoff assist -- his ninth point -- on Gionta's goal. Brodeur scored into an empty net against Montreal on April 19, 1997, joining Ron Hextall as the only goaltenders to score a goal in a playoff game. ... Mike Rupp joined right winger Cam Janssen and defenseman Johnny Oduya as New Jersey's healthy scratches. ... Emery, who improved to 7-2, also shut out Pittsburgh in Ottawa's first-round clinching 3-0 win on April 19. He hadn't allowed a goal at Scotiabank Place since Sidney Crosby scored 11:44 into the third period of the Pittsburgh Penguins' 4-3 win in Game 2, Ottawa's only loss in the first round.