Beverley finished with 20 points and Dwight Howard added 25 with nine rebounds as the Rockets erased an 11-point deficit and racked up a ninth victory in 10 games.
James Harden shook off a hyperextended right elbow to supply 23 points and seven assists.
The Suns had their three-game winning streak snapped despite a career-high 35 points from Goran Dragic.
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