The Kings overcame a five-point Suns lead with 3 minutes to play thanks to Cousins' 3-point play and two free throws during a 10-point run.
The Suns turned the ball over twice and missed their final three shots in the late going.
Cousins ended with 28 points, eight rebounds and six assists. Francisco Garcia added 20 points and 11 rebounds for Sacramento, which won for the second time in three games.
The Suns got 20 points and 12 assists from Steve Nash and Vince Carter added 17 points.