Brown missed two of the three shots, however, and Auburn held on for a 78-77 win to advance to the Round of 32 for the second straight year.
No. 5 Auburn (27-9) led by seven points going into the final minute, but after New Mexico State (30-5) struggled taking care of the ball all game, it was the Tigers who treated the basketball as if it were lathered in butter in crunch time.
Down three points after two Okeke free throws, the Aggies drew a foul, but missed one of the freebies from the charity stripe, to give Auburn a two-point lead before foul shots pushed it to four points.
With the clock ticking down, Harris passed on an open layup and kicked out to wide-open teammate Terrell Brown, who was spotted up for the game-winner behind the arc. There was a panicky Chuma Okeke turnover that set up a 3-pointer from Queen with 29 seconds to go to cut the Tigers' lead to one.
"Until you get in that moment, you don't know how you're going to react", Auburn coach Bruce Pearl said, when asked about the Tigers' near meltdown. McCormick ended up with five points, four assists and two rebounds in 23 minutes of action.
Tennessee won a hard-fought game over Kentucky in the semifinals and looked emotionally drained in the title game against Auburn.
Somali: 5 people including deputy minister killed in Al-Shabaab attack
Senator Ilyas Ali Hassan confirmed that Saqar Ibrahim Abdalla, the deputy minister for labour and social affairs, was also killed. The group also claimed responsibility for a March 7 auto bombing near a restaurant in the capital that killed four people.
"New Mexico State if they were playing in the SEC they'd look like us they'd shoot the three ball they'd spread it they do a better job chasing down rebounds than we do they score early they score late they're active and engaged defensively they don't turn over they turn you over", Pearl said.
Auburn will face the victor of No. 4 Kansas and No. 13 Northeastern. Last year, the Tigers won the regular season crown. Three attempts at the charity stripe to win the game.
LSU took on Yale in the No. 3/No. 14 matchup, and the Tigers held on for a 79-74 victory.
Cable and satellite subscribers can watch any of the NCAA Tournament games at the March Madness website or mobile app by logging in with their provider credentials. Backup point guard J'Von McCormick scored a career-high 16 points off the bench.
Florida 70, Nevada 61: Florida almost squandered a double-digit lead before finally stopping a Nevada comeback and pulling off an upset in the first round.