Tyreke Evans missed the game after being suspended for one contest following an off-court incident involving his driving an automobile at high speed. He is expected to return for Sacramento's game in New Jersey on Friday.
Udrih made two free throws to give Sacramento a 117-114 lead, after which Wayne Ellington attempted a 3-pointer that would have sent the game to overtime.
Ellington's attempt misfired and although Wesley Johnson tipped in the rebound just before the buzzer, it left the Timberwolves a point short.
Carl Landry and Francisco Garcia led a balanced attack with 22 points each for the Kings. Udrih had 18 points and first-round draft pick DeMarcus Cousins had 14 in his pro debut.
Minnesota was led by 20 points from Luke Ridnour.