The Kings were trailing 104-101 with 1:40 left in the game when Cousins put home a reverse a layup, cutting the deficit to one point.
Houston's James Harden missed a 3-point try, and Cousins (17 points, 16 rebounds) followed at the other end with a put-back of an errant try by Ben McLemore with 56.3 remaining, vaulting Sacramento into the lead at 105-104.
The Rockets wasted a 38-point, 10-rebound effort by Harden in dropping a second straight.
Dwight Howard supplied 15 points and eight rebounds.
2014: The Year in Music [PHOTOS]