Haukap's match-winning kill also set an Ohio Valley Conference record for a single match.
UNC (26-8) built an early lead as it won the first two games. But the Otahkians (23-8) would not be denied.
For Southeast, Beckemeyer added a career-high 29 kills. Emily Scannell handed out a career-high 80 assists, and Lori Lange rounded out the record-setting effort with a career-high 20 digs.
UNC got 25 kills from Casey Simpson. Krista Buchholz chipped in 19 kills, and Nicole Reis added 10.
Men's Hoops to Take on Kentucky
The UNC men's basketball team gets back into action tomorrow against Kentucky.
The Tar Heels (3-1), who lost to Michigan State on Wednesday, will take on the Wildcats (1-3) at 3:50 p.m. at the Smith Center.
Former Tar Heel Vince Carter, now an NBA
All-Star with the Toronto Raptors, will have his jersey honored Saturday at halftime.