Dunham allowed all five goals in his first start since Feb. 1 as Islanders top goalie Rick DiPietro sat out because of a stiff neck and overall soreness, ending his career-high streak of 18 straight starts.
"(DiPietro is) a big part of their team," Neil said. "We stressed that in meetings before the game. We wanted to get pucks at the net, you know, Dunham hasn't played that much, and I think we did a good job of that."
Ray Emery, who lost his shutout bid with 5:03 remaining, made 28 saves. The Senators won their second straight to move into fourth place in the Eastern Conference with 89 points, one ahead of Pittsburgh.
Chris Kelly and Joe Corvo scored in the second to put Ottawa up 2-0. Neil scored his 11th goal 2 minutes into the third for his 100th career point, and McAmmond made it 4-0 with his 11th just 24 seconds later.
Spezza scored his 29th at 3:16 to chase Dunham, who stopped 23 shots.
"My job is to find the way to stop pucks," Dunham said. "I felt good the first two periods and then just fell apart there for the first three minutes. The puck all of a sudden just found its way into the net quickly and it got out of hand."
The three-goal outburst beat the previous Senators record for the fastest three goals of 1:20, set by Shawn McEachern, Andreas Dackell and Jason York in a 7-1 win over Atlanta on March 21, 2000.
"To be part of that is great," Neil said. "We wanted to come out and play a solid game and for the most part, everyone stepped up and did their jobs."
Dunham has played in only six games since Dec. 15, including Tuesday when he allowed five goals on 32 shots in a loss to Montreal after replacing DiPietro, who was injured in a mid-ice collision with Canadiens forward Steve Begin.
"That's part of the job as a backup, to go in stretches where you don't play," Dunham said.
New York's Miroslav Satan scored on a 5-on-3 at 14:47 of the third and assisted on Drew Fata's goal with 4.2 seconds remaining.
The Islanders, who have lost four of five (1-3-1), are tied with Carolina for seventh place in the East with 78 points, one ahead of ninth-place Toronto and two up on the New York Rangers and Montreal.
Wade Dubielewicz, recalled from Bridgeport of the AHL on Wednesday, replaced Dunham and stopped the eight shots he faced in his season debut.
"We just didn't want it to get out of hand," Nolan said of his decision to pull Dunham. "We need him right now so he's going to be ready next game."
Kelly scored his 14th goal 1:59 into the second and Corvo made it a two-goal lead at 5:53 when his shot went in off the skate of New York defenseman Marc-Andre Bergeron.
DiPietro, who didn't skate with the Islanders on Thursday morning, is day to day. He was struck on the head by Begin's leg after he chased down a loose puck at the Islanders blue line to prevent a breakaway.
The first goalie ever chosen No. 1 in the NHL draft, DiPietro has hit the 30-win mark for the second straight season with a 2.59 goals-against average after signing a landmark, 15-year contract with the Islanders in September.
"Mike Dunham is a great goaltender," Islanders forward Jason Blake said. "It doesn't matter who's in net - Mike, Ricky or Martin Brodeur. If you hang him out to dry, there's not much he can do back there. It wasn't his fault."
Notes: Dubielewicz had been recalled twice previously this season. He dressed for three games without making an appearance. ... The sellout crowd of 19,989 booed when an apparent sixth Senators goal was waved off because of a tripping penalty against Neil 12:49 into the third. A promotion awards a free slice of pizza to fans if Ottawa scores at least six goals and wins.