Kobe Bryant scored 42 points for the Lakers.
The Thunder open the Western Conference finals on Sunday at top-seeded San Antonio.
After getting eliminated by Los Angeles in 2010 and Dallas in 2011 before both of those teams went on to win it all, the Thunder knocked both out on their way to the West finals for the second straight year.
The only other time the franchise made consecutive conference finals was from 1978-80, including Seattle's only NBA title in 1979.
Once there, they'll face the top-seeded Spurs, the only team other than the Lakers or Mavs to win the West in the past 13 years and currently riding an 18-game winning streak.
Westbrook went running to the scorer's table and pumped his fist in the air after his first energizing three-point play, when he was able to flip the ball in after Ramon Sessions fouled him on the fast break.
He converted another after banking in a jumper from the left side despite Sessions slapping him on the arm to make it 82-76 with 1:29 left in the third quarter.
Durant extended the lead with a 3-pointer in the opening minute of the fourth and then hit another 32 seconds later just after Bryant had stepped to the scorer's table to check in after a brief rest.
There was little Bryant could do after he got back in, despite the 13th 40-point game of his playoff career.
After blowing a fourth-quarter lead in Game 4, Bryant had called out forward Pau Gasol to be more aggressive much as he had with Gasol and Andrew Bynum before the Lakers faced elimination in Game 7 of the first round against Denver.
Gasol came through with a monster game 23 points, 17 rebounds and six assists and Steve Blake scored a playoff career-best 19 points to save the Lakers that time. Bryant didn't get nearly as much help against the Thunder.
Gasol took 14 shots, his most of the series, but made only five to finish with 14 points and 16 rebounds. Metta World Peace scored 11 and Bynum 10.
The Thunder got five of their first eight baskets on dunks and controlled the boards early on, grabbing 16 of the game's first 22 rebounds while keeping Los Angeles off the offensive glass for the first 11 minutes.
Bryant had to create all of the offense, scoring 15 of the Lakers' first 19 points and getting all six of his baskets without the benefit of an assist. When others started chipping in, the Lakers went on a 16-7 run to go up 35-32 following Bynum's three-point play.
Oklahoma City scored the next eight points, including James Harden's fast-break dunk, before Bryant got past him for a pair of dunks of his own the first a driving, two-handed reverse jam and the second a two-handed alley-oop slam over Harden.
But Bryant and World Peace both drew technical fouls as the Lakers lost their cool with 31.9 seconds left before halftime when World Peace was called for a flagrant foul against Thabo Sefolosha on a fast break. World Peace used his right hand to strip the ball from Sefolosha as he went up to the basket but then shoved him out of bounds with his left hand.
Sefolosha hit both free throws and Durant capitalized on both shots from the technicals World Peace and Bryant got for arguing the flagrant call to put the Thunder 54-51 ahead at halftime despite shooting less than 40 percent.
In short OKC back in Western finals
R Russell Westbrook's 28 points and Kevin Durant's 25 help the Thunder close out L.A. Oklahoma City will next face San Antonio.