Florida was behind 2-0 after the first period but then scored three unanswered goals, including goals from Shawn Matthias and Scottie Upshall 70 seconds apart in the second period.
Boyes' backhander 4:29 into the final period capped the rally and gave Florida its first win under interim head coach Peter Horachek.
Tim Thomas made 32 saves.
Hampus Lindholm and Andrew Cogliano each scored for the Ducks, who suffered their first regulation loss in 10 games.
Rookie goalie Frederik Andersen was saddled with his first career loss after notching six straight triumphs, yielding three goals on 25 shots.