Spezza set up Heatley's first-period goal and defenceman Joe Corvo's man-advantage goal in the second restored Ottawa's two-goal lead. Spezza netted his 13th goal late in the middle frame to make it 2-0 and send the Senators on the way to their fifth straight win over the Islanders.
Heatley added his 18th goal with 7:50 left to make it 4-2.
That prevented New York from extending its slim edge in the Atlantic Division. The Islanders are on top of New Jersey and the New York Rangers by one point and haven't owned a bigger advantage in the division since they had a two-point lead on Feb. 18, 1990.
Even with Gerber getting the start over No. 1 goalie Ray Emery, the Senators didn't slow down. They won their fourth straight and for the eighth time in nine outings. Ottawa improved to 27-4 with eight ties against the Islanders since Feb. 12, 1996.
Mike Dunham, getting the start in place of regular goalie Rick DiPietro, fought the puck throughout and gave up big rebounds. But he kept the Islanders in it early when Ottawa held a 17-4 shots advantage through the first period. He finished with 31 saves.
Andy Hilbert's first goal of the season brought the Islanders within 2-1 at 9:38 of the second period but Daniel Alfredsson found Corvo cutting to the net and hit him with a backdoor pass that was steered in at the right post with 49.4 seconds left in the frame - just eight ticks into Ottawa's third power play.
Jason Blake made it 3-2 at 6:42 of the third, doing the grunt work to set up the goal, too. Blake checked Anton Volchenkov hard into the boards, forcing a turnover and leaving the Ottawa forward with an injured arm. The puck went behind the net to Bruno Gervais, who made a quick pass in front to Blake, who scored his 15th goal.
Volchenkov was back for his next shift, but captain Alfredsson didn't return after injuring his leg on a check by Tom Poti behind the Islanders net four minutes into the third. He struggled to get to the bench and then gingerly skated to the dressing room after the next whistle.
Gerber was sharp despite seeing little action through the first half of the game, and made 24 saves. He even turned aside Viktor Kozlov, who scored six goals in two games - including a four-goal effort Sunday in the Islanders' 7-4 victory against the Rangers.
Emery has gotten the bulk of recent work, going 7-2 while starting nine of the previous 10 games. Gerber won his second straight, both in the past week.
Spezza played a strong game throughout, setting up Heatley's team-leading 17th just 4:32 in and ripping in a hard shot from the top of the left circle with 1:33 left in the period.
Notes: This is the latest the Islanders have owned sole possession of first place since Dec. 14, 2001. ... Hilbert's pervious goal came 26 games earlier on April 17 for Pittsburgh against the Islanders. ... DiPietro sat out with an undisclosed lower body injury but is expected to play Thursday against Montreal. ... The Senators, 4-0 against the Islanders last season, have outscored opponents 38-18 the past nine games.