"We were forcing things our last game," said Zajac, who scored the game winner late in the second period. "We weren't supporting each other as well as we normally do and we just got back down to basics, got some shots on net, crashed the net and got some goals."
Parise said the line, which also includes Jamie Langenbrunner, also got more aggressive.
"Believe it or not, we're pretty smart guys," Parise said. "We knew that we didn't play well last game and we needed a better effort tonight, especially if we want to be an effective team. That's why we got the goals and more chances."
Lemaire still expects more from the defending Atlantic Division champions, noting their was too much inconsistency.
Jack Hillen and Mark Streit scored goals for the Islanders (2-5-1) in a game that featured five fights, including three with New York forward Joel Rechlicz. Dwayne Roloson made 16 saves for the Isles.
Both teams will open the regular season on Saturday night at home. The Devils will play the Philadelphia Flyers and the Islanders, who rested several starters, will face the Stanley Cup champion Pittsburgh Penguins.
After giving up power-play goals to fall behind 1-0 and 2-1, the Devils scored twice in the final six minutes of the second period to take a 3-2 lead.
Rolston made a great play on the game-tying goal. He played the puck off the side boards, skated around defenseman Radek Martinek and beat Roloson with a shot between the pads for a power-play goal.
"The biggest thing we take out of this game is understanding we're up 2-1 and we're in controlling play in the second period," Islanders coach Scott Gordon said. "To take a penalty in the offensive zone, that's when the ball starts rolling against us."
Zajac made two plays to give New Jersey the lead with 2:01 left in the period. He kept a clearing pass in the Islanders' zone, fed the puck to Parise along the goal line and then took a return pass and beat Roloson.
Shanahan put the game away with about 8 minutes to play by one-timing a pass from Nicklas Bergfors.
"We have a few more days to go," Brodeur said. "We'll be ready when the time comes. It's a work in progress."
Hillen gave New York its first lead 62 seconds into the second period with a shot from the left circle that Brodeur appeared not to see.
Parise tied the game 1-all four minutes later, stuffing the rebound of Langenbrunner's shot under Roloson.
Streit, who led the Islanders with 10 power-play goals last season, connected on a two-man advantage at 10:18.