Houston ended a two-game skid against a team that has won just twice in its last 21 contests.
Orlando took a 100-98 lead with 5:10 to play on a layup by Nikola Vucevic before the Rockets touched off the outburst that wrapped up their win.
Beverley put Houston in front for good by making a 3-pointer with 4:55 remaining and James Harden contributed six points during the run -- four of them coming at the foul line.
The Rockets built their lead to 109-100 before Orlando could stop the surge.
Tobias Harris came off the bench to score 27 points for the Magic.
Swim Week Miami Beach 2014 [PHOTOS]