Love forced the first overtime by raining in a 3-pointer from the left wing with 1.0 second left in regulation.
This came after Durant hit an indefensible, step-back 3-pointer with 3.9 seconds left to give the Thunder a 116-113 lead.
With 10.1 seconds left in the first overtime, Durant hit a 3-pointer from the right corner to tie the score at 129.
OKC dominated the second overtime 20-11.
"Sometimes this game is crazy," Love said. "If we would have won, you would have looked at the other side and saw 45 and 40 in a loss. Everybody made plays when they counted. It was just a concerted effort from their team in that second overtime. The ball bounced their way with a little bit of luck, they made stops."
Making Minnesota's effort even more impressive was the fact it came on the final stop of a seven-game road trip that began March 12. In addition to missing Pekovic, the Timberwolves also were without rookie point guard sensation Ricky Rubio (out for season with torn ACL) and Michael Beasley (toe).
Despite Minnesota's obvious fatigue, Love said he and his teammates felt confident coming into the game.
"There's just something in my mind that every time I take the floor I feel we have the upper hand, regardless of who we're playing," Love said. "They're one of the top 2, 3, 4 teams in the NBA, the top team in the West, regardless who we play, we always feel like we can beat them."
It's hard to imagine a team losing despite having a 51-point scorer and a triple-double man.
"Against Oklahoma, that can happen," Barea said, forcing a smile. "They're a great team. They're going to keep coming."
Love said he found no solace in breaking Kevin Garnett's franchise record of 47 points.
"We needed this game," Love said. "This definitely could have been a driving force for us in these last 17 games. It's a tough loss … (It) just goes to show there's still a lot of fight left in us. We might be down, but we're not out."