Beverly came off the bench Tuesday night against Bryant, scoring two points in a 95-72 win.
"I was very excited," Beverly said. "The first two games, I was seeing signs and posters, everybody yelling, 'Free Braxton!' Finally I'm free. It was a great feeling. To have that support, it's amazing."
The NCAA had twice denied his request for a waiver. Beverly attended summer school at Ohio State this past summer and then transferred to NC State after former Buckeyes coach Thad Matta was fired in early June.
Last week, Beverly retained an attorney, and the school resubmitted the waiver to play this season.
"Braxton is absolutely thrilled with the NCAA's decision to make him immediately eligible to compete for NC State this season," Beverly's lawyer, Scott Tompsett, said in a statement Tuesday.
"Braxton wants to thank the NCAA for carefully considering NC State's Request for Reconsideration and permitting him to play this season. He is very grateful.
"Braxton also appreciates the public support he's received from so many people across the country and the media outlets that have reported on his case."
Beverly made 1 of 7 shots and missed all three of his 3-point tries in 16 minutes Tuesday.
"I put him in a tough spot," coach Kevin Keatts said. "I could have waited and probably played him on Thursday, but I was so excited. I wanted to see him out there."
Beverly is a 6-foot guard from Kentucky who attended Hargrave Military Academy -- the prep school NC State coach Kevin Keatts led from 1999 to 2001, and also from 2003 to 2011. Wolfpack assistant A.W. Hamilton coached Beverly last season at Hargrave.
Information from The Associated Press was used in this report.