The game was the Thunder's first since the team moved from Seattle to Oklahoma City during the offseason.
The Thunder led 71-62 with 9:54 remaining, but McCants scored 11 of Minnesota's next 14 points, tying the score at 76 with a dunk with 4:45 remaining.
"I had a pretty rough first half," McCants said. "I really couldn't get it going. I got in foul trouble. My teammates carried me. I needed to get to the line a little bit more."
Two free throws by McCants and the consecutive 3s by Carney and Gomes gave the Wolves an 84-78 lead with 2:23 remaining.
A basket by Chris Wilcox pulled the Thunder to 84-80 with 2:11 remaining, but Sebastian Telfair made a basket and two free throws to finish the scoring for Minnesota, which had a 22-60 record last season.
"In the fourth quarter, coach puts the players on the floor he knows can sustain runs, play defense, put some points on the board," McCants said. "In the fourth quarter we did all those things. We made stops.
"We withstood their runs and we were able to make one of our own and then were able to keep the lead. In the past, we weren't able to do those things. We'd get up and when we'd lose the lead we'd be finished for the rest of the game."
Damien Wilkins led the Thunder with 19 points, including a layup to tie the score at 78 with 3:04 to play. McCants fouled out on the play, but Wilkins missed the free throw. Wilcox added 17 points for the Thunder, Russell Westbrook had 13 and Kevin Durant finished with 10 points and seven rebounds.
Oklahoma City led 41-40 at halftime after trailing by as many as 12 points in the first quarter.
"We dug a big hole early. I was really happy with the way we got back in it on defense," Thunder coach P.J. Carlesimo said. "The defense was good until five-minute mark in the fourth quarter. Then we just did a very poor job. We fouled and compounded it with sloppy execution. You can't turn it over the way we did."
Still, he said he was encouraged with the team's effort after seven days of practice.
"I don't like the loss," Carlesimo said. "I especially don't like the way we lost."
But he was happy to hold the Timberwolves to 88 points after they scored 117 in a win over Milwaukee on Monday.
Timberwolves coach Randy Wittman said his team played solid as a group, despite some shooting troubles.
"That was a good game to still grind out a win when you shoot 37 percent," he said.
Durant made the first basket for the Thunder with 11:03 left in the first quarter. ... Wilcox followed with an alley-oop dunk on an assist by Nick Collison at the 10:32 mark.