In the first ever playoff game in Oklahoma City, Durant had 29 points and 19 rebounds. Durant and Russell Westbrook scored 22 of the final 23 for the Thunder, including every point during a 10-2 surge that put Oklahoma City ahead to stay.
The top-seeded Lakers got back within 98-96 with 13.5 seconds left, but the Thunder closed it out from the foul line to re-ignite the series. Game 4 is Saturday in Oklahoma City.
Kobe Bryant scored 24 points to surpass Jerry West's Lakers franchise record for playoff scoring, and Pau Gasol had 17 points and 15 rebounds for Los Angeles.
Undaunted by a raucous sellout crowd, the top-seeded Lakers scored the first 10 points of the game and were in control until the Thunder roared back with an electrifying run of eight straight points late in the third quarter.
The fans reached a deafening pitch as the Thunder completed their charge back from an 11-point deficit. James Harden and Durant hit back-to-back 3-pointers to tie it at 74, and Oklahoma City finally took its first lead of the game with its opening possession of the fourth quarter.
Andrew Bynum pulled Los Angeles even for the final time by powering through a hard foul for a dunk, then hit the ensuing free throw to tie it at 80.
Durant answered at the other end with a jumper from the right side with 8:41 left to give Oklahoma City the lead for good.
In Chicago, the hosts saw their 21-point lead whittled to one, but hung on the beat Cleveland and make it 2-1 to the Cavaliers after three games.
Derrick Rose scored 31 points and Kirk Hinrich added 27 for Chicago.
Hinrich, a career 80.9 percent foul shooter, missed two with 26 seconds left and the Bulls up 104-99.
Cleveland star LeBron James then buried a 3-pointer with 11 seconds remaining to make it a two-point game. The Cavaliers immediately fouled Rose, who missed the first free throw before converting the second to make it 105-102 with 10.1 seconds left.
Chicago fouled Anderson Varejao to prevent a 3-point attempt, and he made the first but missed the second. Brad Miller got the rebound and converted both foul shots to make it 107-103.
A Mo Williams 3-pointer brought it back to a one-point game with 3.8 seconds left.
The Cavaliers immediately fouled Luol Deng, who hit the first free throw but missed the second.
Cleveland's Anthony Parker got the rebound and raced up the right side but missed a 3-point attempt at the buzzer, and the Bulls escaped with the win.
They will try to tie the best-of-seven series on Sunday.
James scored 13 of his 39 points in the fourth quarter but also committed some late turnovers.
In Portland, Oregon, Jason Richardson scored a playoff career-high 42 points as Phoenix dominated Portland from the start to take a 2-1 lead in their first-round series.
The Suns led by as many as 31 points before Portland mounted a rally in the fourth quarter, closing within 91-80 after Rudy Fernandez hit three consecutive 3-pointers.
The burst came too late for the Blazers, who suffered a setback when starting forward Nicolas Batum aggravated a shoulder injury in the first half and did not return.
Game 4 is Saturday at Portland.
Home-court advantage meant nothing for the Blazers. The fans even booed their team as the players left the court with a 66-37 deficit at the break.
Portland was dismal from the free throw line, making just 16-of-28 attempts.
Amare Stoudemire had 20 points for the Suns, while Steve Nash finished with 13 points and 10 assists.
LaMarcus Aldridge led the Blazers with 17 points. Andre Miller, who scored 31 in Portland's Game 1 win, was off for the second straight game and finished with just 11.
