The uplifting win for the T-Wolves, coming off a pair of losses on a California road trip, snapped their own 12-game losing streak against Oklahoma City.
The NBA-leading Thunder battled back after trailing by 14 to move within a point at 76-75 early in the fourth before Barea took over.
Sinking long three-pointers and scrambling under the hoop, Barea scored 10 points in a 12-2 run that restored Minnesota's double-digit lead at 88-77 and then helped the T-Wolves hold off the Thunder the rest of the way.
"The fourth quarter for us has kind of been our Achilles heel this whole season, but we fought through and J.J. Barea was awesome tonight," said Minnesota's All Star forward Kevin Love.
The loss dropped Oklahoma, last year's losing NBA Finalists, to 21-5 while Minnesota improved to 13-11, seven games behind the Thunder in the Western Conference's Northwest Division.
Love led Minnesota with 28 points and 11 rebounds, and centre Nikola Pekovic of Montenegro had 24 points and 10 boards, while Puerto Rico's Barea came off the bench to score 18 points.
Three-time scoring champion Kevin Durant paced the Thunder with 33 points, and Russell Westbrook added 30, but Oklahoma City's reserves contributed just seven points in all.
"This is a big win here against one of the top teams in the league," said Love, a team-mate of Durant and Westbrook on the US basketball team that won gold at the London Olympics.
"We learned we can fight through and beat any team in the league if we're playing well.
"Soon as guys really get in shape, get back healthy, and Ricky (Rubio) starts playing the way he's capable of playing and gets back from that injury, we're going to be a lot better team."
Spanish guard Rubio, working his way back from a serious knee injury, played 18 minutes without scoring for Minnesota but handed out three assists and had three rebounds.
The Timberwolves used brisk ball movement to spring Pekovic for easy layups and set up Love for open looks beyond the three-point arc as they went on a 19-6 run for a 25-11 lead in the first quarter.
Oklahoma City closed within seven points in the second quarter and got within five after intermission but Minnesota responded each time to restore a cushion, with Barea doing the job in the fourth quarter.
Next up for the Thunder will be a Christmas Day rematch against NBA champions Miami.
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