Marshall sophomore guard DeAndre Kane poured in a game-high 29 points on 12-of-22 shooting with four rebounds, four assists and two steals.
"[Belmont] never goes away,'' said Kane. "If you watch the games they've played, they're down 10 points almost every game. We got a little careless with the ball in the second half and they hit some big 3s and got back into the game.''
Tinnon added 24 points, including sinking all eight of his free throws, and landed 10 rebounds and blocked two shots for the Herd, which shot 47.8 percent from the field.
The Herd shot 51.4 percent in the opening half as it built a 46-39 advantage and needed every bit of that as it withstood the Bruins' final flurry.
Johnson finished with 18 points, including making all 10 of his free throws, to lead six Belmont players in double figures. The Bruins, who converted 25-of-29 at the charity stripe, held a 27-5 edge over the Herd in points scored off the bench, and shot 50 percent in the second half.
Marshall looked as if it was going to put the game away about midway through the second half, taking leads of 66-53 and 70-57. From the 8:36 mark on, the Bruins began chipping away at the Herd's advantage, pulling within four points on four straight trips down the floor before taking a one-point lead on Barnes' two foul shots with 1:26 to go.
"If you're a fan it's a great game,'' said Belmont associate head coach Brian Ayers, who was filling in for head coach Rick Byrd after he was ejected from the team's last game.
"Marshall is a difficult team to go against. Their athleticism in the lane, their offensive rebounding, you've got to step up and make shots.''
Marshall, which played Belmont for the first time in school history, will visit the Bruins on Dec. 29 in Nashville, Tenn.
"I'm hoping my back goes out so I don't have to make that trip,'' joked Herrion. "These are the types of games that are going to help you get ready for conference play.''
Belmont competes in the Atlantic Sun Conference ... Byrd is in his 26th season as Belmont's head coach and owns a 617-337 career record in 31 seasons overall ... Marshall junior guard Shaquille Johnson needs 20 points to become the 48th player in school history to surpass 1,000 career points ... The Herd will host West Virginia University Tech at 7 p.m. Wednesday. That will be Marshall's third game in five days.