The Clippers, who entered the fourth quarter with a 12-point lead, saw their advantage cut to two, 96-94, with 7 minutes 30 seconds left after the Suns went on a 17-7 run.
The Clippers then went on a 15-0 run to take a 111-94 lead with just under four minutes left.
Blake Griffin had 23 points, seven rebounds and seven assists for the Clippers. Chris Paul finished 23 points, 12 assists and eight rebounds. J.J Redick contributed 20 points and DeAndre Jordan had 18 points and 14 rebounds.
Isaiah Thomas led the Suns with 25 points.
The Clippers outshot the Suns from the field, 49.4% to 42.5%, and from beyond the three-point line, 43.5% to 34.5%. The Clippers also outrebounded the Suns, 50-31.
Spencer Hawes made consecutive three-pointers in the third quarter to give the Clippers their biggest lead to that point, 85-72, with 1:52 left. He finished with 11 points on four-for-six shooting.
The Clippers (30-14) defeated the Suns (26-20) for the third time in three tries this season.
The Clippers will play the Denver Nuggets on Monday at 7:30 p.m. at Staples Center in the second leg of a back-to-back set. After Monday's game, the Clippers leave for an eight-game trip.