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.
Susan Sarandon 'very excited' about daughter's pregnancy
Dennis Rodman pledges to end trips to North Korea