Rashad Whack had 20 points and Julian Norfleet scored 17 for the fourth-seeded Mountaineers (16-16), who have won four straight. Taylor Danaher and Sam Prescott added 15 points apiece and Will Miller contributed 11 points off the bench.
"We had a lot of confidence," Mount St. Mary's head coach Jamion Christian said. "There was a calm to these guys, especially after the last two days."
Karvel Anderson poured in a game-high 21 points for the top-seeded Colonials (21-13) and Lucky Jones and Charles Oliver scored 11 apiece. David Appolon added 10 points in defeat.
"Mount was the better team tonight," said Robert Morris head coach Andrew Toole. "I'm disappointed for our team. I wish we would have played better."
Mount St. Mary's took control right from the tip. They led 16-8 with 12:22 left in the first half before a 21-9 tear staked the Mountaineers a 20-point lead, 37-17, with 6 1/2 left in the half.
Robert Morris trailed 48-32 at the break after trading baskets to close out the final five minutes of the half.
The Colonials trailed 57-47 with 12:44 left to play in the second half, however, the Mountaineers slowly stretched their lead to 76-57 with 6 1/2 left on the clock.
The Mountaineers led by as many as 21 down the wire and never trailed in the contest to book their first trip to the NCAA Tournament since 2008.