Bairstow scored a career-high 29 points, and Kirk had 24 points and 13 rebounds to help No. 22 New Mexico beat Charleston Southern 109-93 on Sunday.
"I thought their size was a significant difference in the game," Buccaneers coach Barclay Radebaugh said.
"I thought they executed extremely well. They're a very good team. They're a legitimate top-20, top-15 team. And certainly their size presented us with a lot of problems."
The two big men each went 9 for 13 from the field. Kirk added five blocks, and Bairstow drew 10 fouls and went 11 for 16 from the line.
"I'm really proud of the way Bairstow and Kirk played," New Mexico coach Craig Neal said.
Kendall Williams had 20 points and 10 assists for the Lobos (2-0).
Overall, Neal said it wasn't the Lobos' best effort on the defensive end.
"I'm not real happy," he said. "As a matter of fact, I'm a little bit embarrassed with the way we guarded in the second half. ... In the first half, I thought we did a really, really good job of playing the way we wanted to play. We did a nice job of holding them to 36 points. We did what we wanted to do."
Charleston Southern led 21-19 following a 3-pointer from Arlon Harper to cap an 11-4 run. But Bairstow started a 9-0 burst with a dunk. The Lobos were up 35-29 with 7 minutes left in the first half before using a 15-3 run that included five points from Bairstow to take control.
They never let the lead dip below double figures the rest of the game.
Saah Nimley scored 24 points to lead the Buccaneers (2-2). The 5-foot-8 guard was 15 of 17 from the line.
"I like the way they play," Neal said about the Buccaneers. "They've got really good guards and the little guy can play and he's got a big heart."