Danny Thompson's layup with 1:38 remaining gave the Mountaineers a 73-69 lead, but Johnson responded with a 3-pointer, bringing the Bobcats within one point.
Shawn Atupem increased the Mountaineers' lead again with a jump shot, making it 75-72.
The Bobcats improved to 5-2, 1-0 Northeast Conference. The Mountaineers (3-5, 1-1) led by four points with under two minutes remaining, but an 8-2 run by the Bobcats sealed the win.
Lamar Trice led Mount St. Mary's with 17 points, and three other players scored in double figures; Julian Norfleet scored 16 points, Atupem had 15 and Thompson scored career-highs of 12 points and eight rebounds.
Johnson scored the final eight points for the Bobcats and had a game-high 25 points.
Senior forward Tayvon Jackson made his first collegiate start for the Mountaineers, finishing with six points, two rebounds and two assists.
Johns Hopkins 61, Dickinson 60: Adam Spengler tied the game at 60 with 1:26 remaining and made the free throw converting the 3-point play and giving the Blue Jays (2-4, 1-2 Centennial Conference) the one point lead over the visiting Red Devils (3-4, 2-1).
John Alberici scored 14 points and had four blocks for Hopkins, including one on Dickinson's final shot attempt of the game.
Washington College 77, Muhlenberg 76: Junior guard Kevin Breslin converted the game-tying and game-winning free throws for the Shoremen (3-4, 2-1 CC) with 5.6 seconds remaining against the visiting Mules (5-2, 1-2).
There were 10 lead changes, five ties and neither team led by more than five points in the second half. Breslin finished 8-for-8 from the free throw line and led the Shoremen with 24 points.
Hillary Haley led UMES with 16 points.
Hofstra 74, Towson 62: The Tigers (2-4, 0-1 Colonial Athletic Conference) couldn't handle the league's leading scorer, Charles Jenkins, who scored 21 of his game-high 26 points in the second-half comeback for the Pride (4-3, 1-0).
Morgan State allowed only 13 points in the first half and led by 22 points at halftime. Brittany Dodson scored 12 of her team-high 15 points in the second half to hold off Coppin State.
UMBC 63, Bucknell 57: Junior guard Michelle Kurowski scored 25 points, including seven in the final 3:15 of the game, to lead the Retrievers (3-5) to a come-from-behind victory over the visiting Bison (2-5).
UMBC trailed 54-43 with under 10 minutes remaining. Kurowski made two free throws to start the 20-3 run to end the game.
Towson 78, Rhode Island 72: Krystal Parnell (21 points) and Charmonique Watt (18 points) combined to score 39 points, and the host Tigers (4-3) recorded their second straight win.
"Krystal really proved what a good point guard she is today and the offensive effort from she and Charmonique was a nice lift," said Towson coach Joe Matthews.
Pittsburgh 66, Mount St. Mary's 30: The Mountaineers (1-5) led 3-2 early but a 22-2 run by the Panthers (4-3) created a lead they couldn't catch.
The Rams fell to 4-4.
Bowie State 69, Bloomsfield 61: Briana Taylor scored 18 points and Brittney Jackson had 15 to power the host Bulldogs (2-0) past the Deacons (1-4).
The score was tied once at 2 with 17:15 left in the first half. Jackson hit a 3-pointer with 16:30 left to give Bowie the lead for good.
Johns Hopkins 58, Dickinson 38: The Blue Jays (7-2, 3-0 CC) held the visiting Red Devils (3-3, 1-3) to 11 second-half points to win their seventh straight game. Siobhan Callanan led Hopkins with 15 points and seven rebounds, and Lyndsay Burton added eight points and 15 rebounds.
Franklin & Marshall 59, McDaniel 37: Senior Whitney Snoops recorded a double double, scoring 12 points and grabbing a career-best 16 rebounds for the Green Terror (0-6, 0-4 CC) against the visiting Diplomats (3-3, 2-1).
Marywood 81, College of Notre Dame 28: The host Pacers (5-1, 2-0 Colonial States Athletic Conference) opened the game with a 17-0 run and never looked back. Marywood's Lauren Rogan had 16 points, and Brittany Mang had 15. India Scott had a game-high 19 points for the Gators (1-6, 0-2).
Muhlenberg 68, Washington College 47: The host Shorewomen (3-4, 1-2 Centennial) saw their 29-27 halftime lead evaporate in the opening minutes of the second half as the Mules (6-0, 3-0) went on a 7-0 run to take the lead for good.