The Terrapins (5-3) trailed 70-69 with 2:53 remaining against a team that lost to Marquette by 54 points and to Minnesota by 29.
Stoglin put Maryland up with a jumper, then added another to make it 73-70 with 1:48 left. After Josh Castellanos sank a layup for the Mountaineers, Stoglin missed a runner in the lane, giving the Mountaineers a chance to take the lead.
Thompson dunked with 2.3 seconds left for the Mountaineers, but Sean Mosely clinched for the Terps by making two foul shots with 1 second remaining.
It was the first of six straight non-league home games for the Terrapins, who have been decidedly inconsistent in coach Mark Turgeon's first season.
That's how it was in this game.
Maryland led 45-29 shortly before halftime and 59-52 with 9:55 left before the Mountaineers went on a 9-0 run to go in front for the first time.
Norfleet scored 18 for the Mountaineers (1-7), who have lost six straight. The Mountaineers are 1-21 against Atlantic Coast Conference teams, including 0-7 against the Terps.
Earlier in the day, Mountaineers coach Robert Burke dismissed senior guard Lamar Trice for violating team rules. Trice totaled 20 points in Mount St. Mary's previous two games after serving a five-game suspension at the outset of the season. He finished his career with 508 points in 83 games.
Stoglin scored 13 points in the first half, going 3-for-3 from the floor and making 7 of 8 foul shots to help the Terrapins go up 45-32 at the break.
Maryland committed only two turnovers and outscored Mount St. Mary's 14-2 at the foul line, but the Mountaineers went 6-for-9 from 3-point range to stay within striking distance.
Mount St. Mary's clicked on three of its first five attempts from beyond the arc and trailed 15-13 before Stoglin made four free throws and Mosley popped a 3-pointer to make it 22-13.
It was 27-20 before Nick Faust, Padgett and Mosley scored successive baskets to provide the Terrapins with a 13-point cushion