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.
Mike Dunham allowed all five goals in his first start since Feb. 1 as Islanders No. 1 goalie Rick DiPietro sat out because of a stiff neck and overall soreness, ending his career-high streak of 18 straight starts.
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.