Bairstow had 22 points and 11 rebounds, Kirk added 16 points and 12 rebounds, and the 23rd-ranked Lobos opened the season with an 88-52 victory over Alabama A&M on Saturday night.
"It was big night for me," Neal said.
Kendall Williams added 17 points and seven assists for New Mexico (1-0) and Cullen Neal, son of the head coach, finished with 12 in his college debut. Bairstow shot 9 for 10 from the field and Kirk was 7 for 13.
Alabama A&M couldn't control New Mexico's interior players as the Lobos jumped out to a 10-0 lead then stretched it to 21-3 with Bairstow contributing eight points in the stretch.
The lead didn't drop below 15 the rest of the way.
Jeremy Crutcher had 17 points to lead the Bulldogs (0-1). No other teammate scored in double digits.
"They're a good team," Bulldogs coach Willie Hayes said of New Mexico. "They have size. They shoot the ball."
New Mexico committed just nine turnovers while shooting 58.5 percent. The Lobos, who had 19 assists, also had a 48-27 rebounding advantage and held the Bulldogs to 26.8 percent shooting.
"I thought the guys played with a tempo that we wanted to see and I think we saw a team that plays together and sacrifices for each other and plays to a high level," Neal said. "I think we shot the ball well."
New Mexico demonstrated an up-tempo pace that it seldom used in previous years under former coach Steve Alford, who left for UCLA during the offseason.
"I thought it would be a good test because they had 11 guys coming back, veteran guys," Neal said. "I just thought we pushed the tempo in the first half but once we got to a certain number I just didn't see any reason to push the tempo again."
Although the Bulldogs didn't up much resistance, Hayes said it's a game that will be beneficial.
"This is going to help us as the season progresses," he said. "It shows you a bit of what you have to get better. We have to get better at rebounding."
New Mexico also had 16 second-chance points.
"We were able to get rebounds and get out and go," Bairstow said. "We did a much better job of defending."
That was something Neal saw, as well.
"I think we also played very good defense," he said. "That's one thing we're going to continue to do. And I thought everybody played really hard. Everybody that got in the game played really hard."
Maryland point guard Melo Trimble has withdrawn from the NBA draft and will return to College Park for his junior season.
Louisville's Chinanu Onuaku, who recently underwent a medical procedure to correct a heart rhythm issue detected during the combine, will keep his name in the NBA draft pool.
Andrew White III will return to the Nebraska men's basketball team next season after removing his name from the NBA draft.