The Terrapins, ranked No. 17 in the National Soccer Coaches Association of America preseason poll, were held off the scoreboard for nearly 18 minutes as Bulldog starting goalkeeper Naomi Carter made three saves in that span.
Maryland finally got on the board when Spivey scored off a corner kick with 17:40 expired in the first half. She added a second goal seven minutes later, and Lauren Berman also found the net as the Terrapins took a 3-0 lead into halftime.
Carter finished with four saves over the opening 45 minutes and had seven in the game before being relieved by Sarah Katchen with 20 minutes remaining. Katchen made a pair of saves in her time in goal.
Spivey, a sophomore who was the No. 6 recruit in the nation two years ago, completed her hat trick at the 53:47 mark.
"Maryland is a very good team. They have some very talented soccer athletes," said Citadel head coach Bob Winch. "Our girls worked hard until the final whistle."
The majority of the play took place on The Citadel side of the field as the Terrapins finished with a 34-1 advantage in shots and 11-0 in corner kicks. Andrea Davila was wide of the goal late in the first half for the only shot attempt by the Bulldogs.
The Citadel completes its two-game road trip to open the season on Sunday at noon against defending Patriot League regular season champion Navy. The Bulldogs play their home opener next Friday against Jacksonville State, with kickoff at 4 p.m.