Dany Heatley and Jason Spezza scored for Ottawa. The Senators have lost four straight games for the second time this season.
Alex Auld made 28 saves for Ottawa.
The first period was scoreless, mostly thanks to MacDonald, who faced eight of the first nine shots of the game, and 15 overall in the period.
Bergenheim broke through to give the Islanders the lead at 3:54 of the second period. He took the rebound of Doug Weight's shot and quickly flipped it past Auld.
Sim connected on a short shot on the Islanders' first power-play attempt for a 2-0 advantage at 9:54. In the third period, Campoli upped the lead to 3-0 at 3:59 on a center-point wrist shot.
Heatley broke MacDonald's shutout bid at 13:29 with his 10th goal of the season.
With Auld pulled late for an extra attacker, Spezza buried a loose puck with 93 seconds left to close the gap to 3-2.
