Michael Ryan and Jason Pominville scored in regulation for the surging Sabres, who won for the fifth time in six games.
Karel Rachunek and Mike Mottau scored for the Devils, who had their two-game winning streak snapped. New Jersey also lost for the first time in four games on the road.
New Jersey had won the previous three meetings between the two teams this season by shootouts, and also came in having defeated the Sabres in 16 of the past 23 games.
Miller finished with 24 saves, and hasn't allowed more than two goals in his last six starts.
Brodeur had 20 saves.
Ryan opened the scoring just 2:30 into the game with his fourth of the season when he deflected Tallinder's slap shot from the left point past Brodeur for a 1-0 Sabres lead.
Pominville pushed Buffalo's edge to 2-0 with his 14th at 8:04 of the second period. Driving to the left post, Pominville redirected Daniel Paille's pass from the boards along the right circle with his left skate. The goal was upheld after a video review.
Rachunek cut the Sabres' lead to 2-1 with his third with 4:35 remaining in the second. From the left circle, Gionta hit a trailing Rachunek with a perfect feed at the top of the right circle. Rachunek deposited the puck into the top-right corner with a wrist shot.
The Devils used a fortunate break to tie it at 2 with 13:44 left in the third period. Mottau's pass from the right circle to John Madden near the crease was inadvertently knocked in off Miller by Buffalo defenseman Dmitri Kalinin, who was trying to swat the pass away.
