Cousins hit 11 of 15 shots and Ben McLemore had 22 points and nine rebounds to help the Kings overcome a sluggish start and improve to an eye-opening 8-5.
Andrew Wiggins scored a career-high 29 points and had four steals for the Timberwolves, who were missing four starters and playing the second night of a back-to-back.
Kings coach Mike Malone said before the game that of all the games on this four-game road trip that started on Saturday night, this one against a depleted Wolves team scared him the most. The young Kings have been one of the biggest early surprises of the league with eight wins in their first 13 games on the strength of Cousins' level-headed dominance in the paint and Darren Collison's two-way play at point guard.
But Malone was worried about a team that is still learning how to handle success looking at the struggling and short-handed Wolves and not bringing the necessary focus and intensity. His fears proved valid at the start.
Also playing without Ricky Rubio, Kevin Martin and Ronny Turiaf, Timberwolves coach Flip Saunders used a zone defense that befuddled the Kings early on. They missed 10 of their first 12 3-pointers and had difficulty getting Cousins touches in the paint.
McLemore missed three of his four 3s in the first half and five of his first seven shots overall, but got two dunks at the end of the second quarter and one at the start of the third to get himself going. He hit three 3-pointers in a row after that flurry of dunks, then scored on a drive to the basket for a 72-62 lead midway through the third.
Wiggins led a charge that cut the deficit to five with four minutes to play, but Cousins was just too much.
Kings: Rudy Gay had just 14 points and six rebounds in 35 minutes while playing with a sore Achilles. ... Collison had 19 points, seven assists and four turnovers. ... Derrick Williams, chosen No. 2 overall by the Timberwolves in 2011 and traded to Sacramento last year, had 12 points and six rebounds. ...
Timberwolves: Saunders said Pekovic (wrist, foot) will be evaluated on Monday. If it is determined he will be out at least another 10 days, the Wolves could get a roster exception to add another player without trading or releasing a player. ... Wiggins played 19 straight minutes to open the game.
Kings: At New Orleans on Tuesday.
Timberwolves: Host Milwaukee on Wednesday.