Quarterman's triple-double was the first by an LSU player since Shaquille O'Neal did it against BYU in the 1992 NCAA tournament.
Jarell Martin added 18 points and Keith Hornsby 16 for the Tigers (21-8, 10-6 SEC), who won their third straight overall while sweeping the two-game season series with Ole Miss.
Jordan Mickey added 11 points — all in the second half — and blocked four shots.
Stefan Moody scored 15 and Sebastian Saiz 11 for Ole Miss (19-10, 10-6), which came in with a school-record four straight road victories in SEC play.
LSU pulled even with both Ole Miss and Georgia in the league standings. The top four seeds get a double-bye in the SEC tournament.
The Tigers trailed by as many as 11 during a sloppy first half but executed far better during the final 20 minutes.
Early in the second half, Jalyn Patterson's corner 3 gave LSU a 31-29 lead, marking the first time the Tigers had been in front since leading 15-14.
The Tigers continued the onslaught, putting together an 11-0 run, capped by Mickey's first points of the game, which made it 36-29 with about 15 minutes left.
Ole Miss briefly pulled to 44-40 before LSU strung together a 10-2 run that began with Quarterman's three-point play and ended with Hornsby's 3. In between, Mickey scored twice, including a put-back dunk.
Mickey missed his first seven shots, many from inside.
The Rebels raced to the first double-digit lead of the game with 12-0 run that began with Anthony Perez's 3 and ended with his free throw, making it 26-15.
The Tigers settled down after that, however, gradually trimming their deficit to four when Quarterman's free throws made it 27-23, a score that stood until halftime.
Mississippi: Moody was held below the 20.1 points per game average he'd posted during his previous eight games. ... The Rebels, who came in hitting 78.1 percent from the free throw line, went 13 of 21 (61.9 percent) against LSU. ... Ole Miss fell to 10-4 on the road this season.
LSU: LSU took only its third victory in the last nine meetings. ... The Tigers improved to 13-3 at home. ... The victory clinched LSU's first winning conference record since the 2008-09 season, which was also the last time LSU made the NCAA tournament.
Mississippi: Visit Alabama on Tuesday night.
LSU: Host Tennessee on Wednesday night.
AP: LSU 73, Ole Miss 63
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