The Bruins ended a three-game losing streak in the first outing on a six-game road trip.
Wheeler's goal was followed by scores from Mark Recchi and Gregory Campbell to give Boston a 3-0 lead after one period. David Krejci added a backhander 55 seconds into the middle period before the Islanders could get on the board.
Boston answered each of the first two New York goals with another of its own, including a power-play tally by Milan Lucic that gave the Bruins a 6-2 lead midway through the second. It was Lucic's 24th goal of the season.
Tuukka Rask earned the victory by making 34 saves. Boston has defeated the Islanders in 10 of their last 12 meetings.
New York, which had a four-game winning streak snapped, got two goals from John Tavares. Nate Lawson gave up five goals on 18 shots before being removed in favor of Al Montoya. It was the eighth start of Lawson's career.