The Kings led by as many as 11 in the fourth quarter, but Minnesota went on a 17-7 run and moved within a single point on a 3-point play by J.J. Barea with 4.6 seconds remaining.
After Thomas made his free throws, Barea missed a 3-point try that left the Timberwolves with their second straight loss.
Sacramento won on the road for the fifth time in 15 tries.
Rudy Gay hit 12-of-19 shots and scored 33 points to lead the Kings, who shot 54 percent from the field. Thomas added 26 points and seven assists while DeMarcus Cousins had 20 points and 11 rebounds. It was the 12th straight double-double for Cousins.
Kevin Love had 27 points and 11 rebounds for Minnesota.
Celebrity Families of 2014 [PHOTOS]