Following another Utah turnover, Mershon, who missed nine of her first 10 shots, hit two free throws to put the Dragons up by three with 9.7 seconds left.
The Utes then put the ball in the hands of their leading scorer, but 6-foot-4 junior forward Michelle Plouffe, who averaged 21.6 points and 13.8 rebounds through Utah's first five WNIT wins, misfired on a 3-point attempt at the buzzer.
Plouffe finished with nine points on 3 for 14 shooting but gobbled up a game-high 14 rebounds for the Utes (23-14), who were playing their fifth WNIT game on the road and their first game of the season in the Eastern Time Zone.
Afterward, Utah head coach Anthony Levrets called playing in Drexel's intimate and loud home gym "fun" but revealed that so much traveling wore his team down.
"We have literally traveled almost 7,000 miles and spent 18 hours on a bus," Levrets said. "We haven't had a direct flight in a month. It's been really, really hard. But it's been fun. It was a great opportunity for our kids to build a special memory together that they're never going to forget."
Mershon, one of five players at Drexel to reach 1,600 career points, will also leave school with a special memory. And finishing her career with six straight postseason victories is even more gratifying because it came on the heels of Drexel's gut-wrenching 59-56 loss to nationally ranked Delaware in the Colonial Athletic Association finals March 17.
Mershon said the feeling after that loss "sat with her so long." She made sure she never had to go through it again.
"At this point, it's really indescribable," Mershon said. "I'm obviously ecstatic and very emotional. I couldn't have asked for a better way to end my career here."