After road losses in Brooklyn and Boston, the Kings (14-19) persevered without their two best players, who fouled out in the fourth quarter, to finish off the pesky Timberwolves (5-26) 110-107 at the Target Center.
Darren Collison hit two free throws with 2.8 seconds to go and a Troy Daniels 3-point attempt at the buzzer missed.
All five Kings starters were in double figures, led by Collison and Rudy Gay with 21 apiece.
DeMarcus Cousins added 19, Ben McLemore 14, and surprise starter Derrick Williams registered 17.
Andrew Wiggins led Minnesota with 27 points, while Gorgui Dieng and Shabbaz Muhammad contributed 15 points each.
Sacramento was able to finish without its two marquee players as Gay fouled out with 4:21 to go and the Kings up 99-98, and Cousins fouled out at the 2:46 mark with the Kings leading 104-101.
With the game tied at 99, Sacramento outscored Minnesota 11-8 with four points from Collison and three from Williams.
The Kings raced out to a 19-9 lead fueled by seven points from Williams, who was facing his former team.
The Kings led the Timberwolves 37-29 at the end of the first quarter, and 60-58 at the half.
The high scoring first half featured Wiggins going for 21 points while Sacramento’s big three of Cousins, Gay and Collison combined for 34 points -- the total they were held to in Wednesday’s loss in Boston.
The Kings captured their first road win since a 99-89 win in New Orleans on Nov. 22 and can split their current four-game road trip with a win at Detroit on Sunday.
Minnesota has lost 16 of its last 17 and the Timberwolves last won on Dec. 10, 90-82 over Portland.
Darren Collison was clutch at winning-time, leading the Kings on the road and finishing with 19 points and four assists.
With the score tied at 99 with 4:09 remaining, the Kings finished it without Cousins and Gay, outscoring the Timberwolves 11 to eight to get the win.
Kings – F Omri Casspi (left knee bone contusion), G Ramon Sessions (low back strain) and F Eric Moreland (left shoulder labral tear) were out.
Moreland underwent surgery on Wednesday and is expected to be out for the rest of the season.
Timberwolves – G Kevin Martin (right wrist fracture), C Nikola Pekovic (right wrist sprain and right ankle soreness) and G Rick Rubio (left ankle sprain) were out.
WHAT'S NEXT: Sacramento’s four-game road trip wraps up in Detroit on Sunday.