Many fans seemed to think Quarterman was fouled. There was contact, but it could have been tough to tell in real time who initiated it as the Sooners collapsed defensively into the paint.
Quarterman finished with a team-high 18 points, while Craig Victor scored 15. Blakeney finished with 11.
Simmons' driving reverse, two-handed dunk, which whipped the crowd into an arena-shaking frenzy, put LSU ahead 50-38. Soon after, the Tigers took their largest lead, at 14, when Keith Hornsby's jumper made it 52-38.
Oklahoma's comeback started with a jumper by Cousins with 13:41 left, which made it 57-46. That began a 22-8 run that included four 3s by Hield, the fourth calmly drained from the left corner to put Oklahoma up 66-65 with 4:05 remaining.
Hield added yet another clutch 3 from the right wing just moments after snagging an offensive rebound of Cousins' miss. Cousins got the ball back on that possession and kicked it out to Hield for a shot that put Oklahoma up 73-72 with 1:53 left.
The Tigers led nearly the entire first half, when they shot 55.6 percent (15 of 27), including 7 of 12 from 3-point range. LSU was up by as many as 13 points when Blakeney and Quarterman hit back-to-back 3s, making it 36-23.
Jordan Woodard responded with a quick 3 to trim OU's deficit back to 10. Hield, who had 11 points in the first half, added two free throws minutes later to pull the Sooners to 41-36 before Aaron Epps' 3 widened LSU's lead back to 44-36 at halftime.
Oklahoma: Kruger, in his fifth season with the Sooners, reached his 100th victory with the program. ... Oklahoma has hit at least 10 3s in 14 games this season, the most in one season in program history. ... Hield has scored at least 20 points in 12 of 14 games.
LSU: Simmons scored at least 10 points for the 19th time, and with nine rebounds narrowly missed what would have been his 16th 10-rebound game and 16th double-double. ... Simmons had five assists, giving him 102 so far in his freshman season. ... This marked the 10th visit by a No. 1 team to LSU, which has gone 2-8 in such games. ... Victor, who did not play until late December because of the timing of his transfer from Arizona, has scored at least 10 points in 12 of his first 13 games.
Oklahoma: Hosts TCU on Tuesday night.
LSU: Visits Auburn on Tuesday night.