Shannon Brown's season-high 21 points quarter trey for Phoenix's first lead since the opening ahead free-throws, and another pair of freebies to put the game 87, on Thursday.
Channing Frye finished with 12 points, Jared Dudley added 11 and Markieff Morris donated 10 in the win. All three contributed six rebounds for Phoenix, which has won seven of its last nine.
The Suns scored 27 points in the fourth while holding Los Angeles to 12 as they battled back from a 17-point deficit.
Blake Griffin paced all scorers with 25 points and Caron Butler netted 14 for the Clippers, who have dropped four of their last five games at Staples Center.
Earlier Thursday, Los Angeles acquired guard Nick Young from the Wizards for forward Brian Cook and a future second-round draft pick in a three-team trade that also involved the Denver Nuggets.