Alabama has struggled to end the season, losing seven of its final 11 games.
The Terps are looking to make the Sweet Sixteen for the first time since 2017.
The Terps held the Mountaineers to four points on 12.5 percent shooting in the second quarter.
Quinerly scored 14 points and notched 11 assists Monday night.
The Crimson Tide hit 16 threes to dash the Terps' Sweet 16 hopes.
Star sophomores Ashley Owusu and Diamond Miller took over as the Terps advanced to the round of 32.
Alabama won both the SEC regular-season and conference tournament championships.
The Terps are looking for their first Sweet Sixteen appearance since 2016.
The Terps have never lost in the first round under Brenda Frese.
“They deserve just as much as the men do.”