Scott Gomez had two goals and Chris Drury also scored for the Rangers, who could end the series Friday with a win at New Jersey. New York took the first two games on enemy ice before splitting two at home.
The rookie defenseman Staal took a pass from Martin Straka, who provided the Rangers with one of their four one-goal leads, and fired a drive from inside the blue line that got by Brodeur.
Gomez sealed it with an empty-netter with 12.2 seconds left.
Brodeur and the Devils kept Rangers agitator Sean Avery without a goal for the first time in the series, one game after his antics led the NHL to amend a rule on unsportsmanlike conduct.
Avery faced Brodeur and away from the play during a 5-on-3 advantage in the Devils' win on Sunday, waving his arms and stick in the goalie's face - a move deemed illegal the following day.
Henrik Lundqvist made 28 saves and the Rangers beat the Devils for the 10th time in 12 meetings this season.
Patrik Elias scored twice and Mike Mottau got New Jersey even in the third period. Brodeur finished with 34 saves.
The Devils have been outscored in the third period 8-2 in the series and 15-3 in 12 meetings between the teams this season.
The Devils had gone 16 straight games without scoring more than two regulation goals against Lundqvist, but have done it two straight contests including their 4-3 overtime victory in Game 3.
Mottau netted the tying goal 4:37 into the third, wristing a shot from the right circle past Lundqvist, who was desperately trying to get a stick from a teammate after losing his.
The frenzied home crowd that enthusiastically waved white towels after each Rangers goal groaned with extra frustration because the goal was scored moments after Avery was dumped in front. Avery was then held down by the pushing stick of Devils defenseman Bryce Salvador.
New York had taken its third one-goal lead in the second period when Drury deflected in a point shot from Fedor Tyutin. That power-play goal was set up by Avery, who drew a tripping penalty from Colin White as he crashed into Brodeur.
The Rangers had their second straight strong start at home, but unlike their Game 3 loss they turned this one into a 1-0 lead.
New York used its first power play to get a shot through Brodeur. Rangers defenseman Dan Girardi deftly kept the puck in at the left point and moved it Drury, who skated into the high slot. He passed back to Girardi, who slid the puck to Gomez for a redirect at 12:37.
It was the fifth point of the series but first goal for Gomez, who had 21 goals and 44 assists in 97 career playoff games with the Devils before signing with the Rangers last summer.
The Devils tied it 31 seconds into the second period. Elias reached the second of consecutive rebounds left by Lundqvist and scored his first of the night and second of the series.
New York needed a little more than 2 minutes to go back in front. Straka took a pass from Brandon Dubinsky and finished a 2-on-1 to make it 2-1 at 2:53.
Still, the Rangers couldn't extend the lead - instead putting the Devils on their second power play by taking a penalty for too many men. Elias' second of the game came 19 seconds later and tied the game 2-2.
The physical and chippy play that became more prevalent in Game 3 picked up as the second period progressed. Travis Zajac clipped Rangers defenseman Michal Rozsival, drawing a 4-minute penalty that produced only two shots by New York.
Brodeur was whistled for diving after getting bumped into by Fredrik Sjostrom, then flopped again in his crease later when Jaromir Jagr bumped him with his thigh and knocked off the goalie's mask.
That led to a scrum which resulted in roughing penalties for Jagr and Johnny Oduya, who came to Brodeur's defense.
