Sykora opened the scoring with his ninth of the season at 9:52 of the first period. Brodeur sprung Sykora and Elias with a clearing pass up the middle. The veteran forwards weaved through the neutral zone before Elias dropped a pass between his legs for Sykora, who sent a soft shot that rolled in under Miller's pads.
"(I) looked for him to shoot through (defenseman) Robyn (Regehr)," Miller said. "He shot around him."
Sykora snapped a wrist shot over Miller's glove 1:26 into the second period to double the Devils' lead. Dainius Zubrus forced a turnover, and Elias set up Sykora for a one-timer with a perfect pass.
New Jersey signed Sykora to a one-year, $650,000 contract after he made the team following a training camp tryout. His 10 goals are tied with linemate Zubrus and rookie Adam Henrique for fourth on the team.
"I'm getting a chance to play with great players -- Patty and Zubie most games. Each guy brings something different," Sykora said. "Once in a while, you're going to have a game like this."
"He played well," Brodeur said of Sykora, with whom he won the Stanley Cup in 2000. "We brought him in to make a difference offensively. That was what the team was looking for."
Luke Adam appeared to cut the Sabres' deficit to 2-1 with a deflection at 5:28 of the second but the goal was disallowed after a video review showed that Adam struck the puck while his stick was above the crossbar.
"Thought it was good," Adam said. "Thought it was on its way down. It was a bit of a bad angle."
Parise made it 3-0 at 6:55 when he tipped in Mark Fayne's point. Vanek scored Buffalo's lone goal 1:14 later, his ninth point in six games.