NBA Most Valuable Player Shai Gilgeous-Alexander delivered a masterpiece performance to power Oklahoma City over Minnesota 128-126 on Monday, lifting the Thunder to the brink of the NBA Finals.

Gilgeous-Alexander scored a playoff career-high 40 points and added 10 assists and nine rebounds to spark the Thunder, who took a 3-1 lead in the best-of-seven Western Conference finals series with potentially clinching game five set for Wednesday at Oklahoma City.

"Play to our identity on both ends of the floor – if we do that we'll be just fine," Gilgeous-Alexander said. "If not, it could get ugly. So we've just got to be who we are and trust our work and trust our habits."

Jalen Williams added 34 points with 6-of-9 shooting from three-point range and Chet Holmgren contributed 21 points for the Thunder.

"They were amazing tonight," said Gilgeous-Alexander of the duo. "They were confident. They weren't rattled by the moment. There's so much to say about the work they put in, the effort, and the character those two guys have. They deserve these moments. I'm nothing but proud of these two."

The Thunder have not reached the NBA Finals since losing to Miami in 2012 while the T-Wolves have never reached the championship series.

Reserves Nickeil Alexander-Walker and Donte DiVincenzo sparked Minnesota with 23 and 21 points respectively, while Jaden McDaniels added 22 and star guard Anthony Edwards, who tightly guarded all night, managed only 16 on 5-of-13 shooting.

"They are a really good team," said Gilgeous-Alexander. "You try and do a good job on their main guys and their B, C and D guys get off. You've got to try and do the job all the way around. It's harder than it looks."

The Timberwolves surrendered 21 turnovers and allowed the Thunder 19 offensive rebounds.

"You're not going to beat a team like this if you are turning it over 20-plus times and letting them have a bunch of second-chance opportunities, and we knew that," Minnesota coach Chris Finch said.

Oklahoma City won the first two games at home but host Minnesota routed the Thunder in game three, setting up an intense game four.

Both teams were physical and aggressive and hot shooting from the start, with Gilgeous-Alexander and Jalen Williams each scoring 13 points in the first quarter as the Thunder took a 37-30 lead.

Gilgeous-Alexander was 5-of-6 from the floor while Williams was 5-of-8 and 3-of-5 from three-point range.

The Timberwolves hit 12-of-19 and 5-of-10 from beyond the arc in the first quarter, but they also made seven turnovers and Edwards did not take a shot until only 35 seconds remained in the first quarter.

Gilgeous-Alexander had 21 points in the first half as Oklahoma City led 65-57 at half-time while Edwards had taken only two shots and Minnesota had surrendered 13 turnovers.

The Thunder took their biggest lead at 68-57 in the opening seconds of the third quarter but the T-Wolves answered with a 9-0 run, Rudy Gobert scoring four in the spurt, and the Oklahoma City lead was only 90-85 entering the fourth quarter.

Jaden McDaniels sank a left corner three-pointer with 23 seconds remaining to lift Minnesota within 123-121, but Gilgeous-Alexander answered with two free throws to boost the Thunder lead to five with 14 seconds remaining.

Gobert's rebound putback pulled the T-Wolves within 125-123 with nine seconds remaining, but NBA scoring champion Gilgeous-Alexander made 1-of-2 free throws to leave the T-Wolves a three-pointer shy of tying the game with eight seconds remaining.

Minnesota's Naz Reid made two free throws but Gilgeous-Alexander was fouled and sank two free throws to give the Thunder a 128-125 lead.

Edwards was fouled with 3.5 seconds remaining and made the first free throw, then intentionally missed the second, but Gilgeous-Alexander threw the ball down the court and out of bounds with 0.3 of a second to play.

A desperation inbounds play failed and the Thunder secured a hard-fought triumph. (AFP)