Tim Thomas, who came in leading the NHL in goals-against average and save percentage, made 32 saves. He then stopped Mike Santorelli, Stephen Weiss and Evgeny Dadonov in the shootout.
David Krejci had both regulation goals for Boston. Michael Ryder had two assists.
David Booth and Mike Santorelli scored for the Panthers and Michael Frolik had two assists.
Scott Clemmensen, making his seventh start of the season, stopped 40 shots for Florida.
Boston won for the first time in four shootouts, while Florida dropped to 2-1.
Boston trailed 2-1 entering the third period before Krejci tied it at 10:35 off a nifty pass from Wheeler.
Krejci took Wheeler's pass while skating in front of Clemmensen and beat the goalie with a deke to his backhand.
Santorelli broke a 1-1 tie at 15:51 of the second period. His goal was allowed after a video review to determine whether his tip of Frolik's wrist shot from the point was caused by a high stick.
Booth opened the scoring 1:02 into the second when he grabbed a loose puck in the Boston zone, spun around and beat Thomas with a wrist shot from the slot.
Krejci tied it at 9:05 of the second period on a rebound off a slap shot from the point by defenseman Zdeno Chara.
Notes: The game marked the beginning of a five-game road trip for Boston, which also will play at Tampa Bay, Atlanta, Buffalo and Toronto. ... Boston C Brad Marchand missed his third consecutive game because of a lower-body injury. ... Florida C Stephen Weiss and D Bryan McCabe each had five-game point streaks snapped. ... Florida had been the only team in the league without an overtime or shootout loss.