The Thunder went on a decisive 17-8 run over the final 6:18 of the fourth quarter led by Russell Westbrook, who scored 11 of his 28 points in the blitz.
"Both teams really played as hard as they can play," Thunder coach Scott Brooks said, "fighting through every possession."
They also came up with a key defensive stand in the last minute when Kendrick Perkins blocked a shot by Gerald Wallace and Serge Ibaka blocked Andre Miller to preserve a four-point lead.
Westbrook completed the sequence with a layup to stretch the advantage to six.
Kevin Durant struggled in the second half, going 0-for-8 from the field, but scored 21 points for the Thunder and had five blocked shots. Ibaka added 18 points.
"There was a time a few years back that if Kevin goes 0-for-8, there's a good chance that we don't win this game," said Brooks.
"Guys have to step up. There's always going to be a different guy."
Portland were unable to capitalise on Wallace's sizzling 40-point performance, with LaMarcus Aldridge the only other Trail Blazer to reach double digits with 20 points.
"It wasn't enough," said Wallace. "I'd rather take the win than take the points."