Kirk scored seven points during a key 15-3 run early in the second half that pushed New Mexico's lead to 48-33. The Lobos (24-4, 11-2 Mountain West) are one win from clinching the regular-season conference title.
"I think a big key was what our two bigs did," New Mexico coach Steve Alford said.
The Aztecs (20-8, 8-6) got 16 points from Jamaal Franklin, but none of his teammates reached double figures. Franklin and Xavier Thames each went 3-of-13 from the field. San Diego State shot 21-for-58 overall (36 percent), including 4-of-23 on 3-pointers.
During a span of almost 5 minutes, Bairstow went 5-of-6 from the foul line, drove the lane for a dunk and added a short jumper to hold off San Diego State, which had pulled to 52-46 with 7 minutes left.
Kendall Williams, who had 46 points in his previous game, finished with eight points, eight assists and six rebounds for New Mexico.
"They really don't care who scores," Alford said. "It's a team that feeds off of each other."
Although San Diego State controlled the boards, grabbing 15 offensive rebounds to six for New Mexico, the Lobos won the game from the foul line by going 24-for-32 compared to 14-of-21 for the Aztecs.
Colorado State graduate transfer John Gillon has chosen Syracuse, giving the Orange a potential starter at point guard entering the 2016-17 season.
DeSean Murray, who averaged 20.2 points as a sophomore at Presbyterian, will transfer to Auburn to play for coach Bruce Pearl.
Former Kentucky guard Ed Davender, the only Wildcat with at least 1,500 points and 400 assists, has died. He was 49.