The win snapped a 12-game losing streak for the Cougars, who improved to 6-18 overall and 2-9 in OVC play. The Bruins dropped to 13-13 and 7-4.
"A lot of good things happened tonight," SIUE Head Coach Sean Lyons said. "It was a good ballgame and we're glad to come out on top and have a chance to come out tomorrow and win a series."
McCunn's hit plated Jordan Ross and broke a 4-4 tie. Earlier in the at-bat he had been hit by a pitch, but the umpire refused to give him first base.
"He took a great at-bat," Lyons said. "I am glad the umpire kept him the box. He had gotten hit by a pitch (the umpire) kept him there and two pitches later he hits the game-winner."
Belmont reliever Logan Bowen (0-2) allowed the run in two innings of work and took the loss. He struck out three. Connor Etheridge started the game and gave up the first four runs on eight hits over 4 2/3 innings.
Belmont took a 3-0 lead, scoring a run in the first inning and two in the second against SIUE starter Ryan Byrd.
Aaron Goecks got the Cougars on the board with a two-run double in the third inning to cut the lead to 3-2.
The Bruins' Jackson Campbell homered in the fourth to extend the lead to two before Goecks and Aaron Jackson each picked up RBIs in the fifth to tie the score 4-4.
Byrd turned in the longest outing of his season, tossing seven innings. He allowed all four runs and struck out six. The Bruins loaded the bases in the seventh against the SIUE starter, but Byrd struck out third baseman Ben Kocher on a high fastball to end the threat.
"He hadn't lost his stuff," Lyons said of the decision to stick with Byrd to finish the seventh inning. "The pitch count was up and he walked a batter previously which made us talk it through, but his stuff was still there. We felt with how solid he had been up to that point that we should just let him finish it out."
The Cougars outhit the Bruins 11-7 for the game. Ross, Goecks and Bret Fehr each had two hits. Goecks finished with three RBIs.
"Offensively we started to get going a little bit," Lyon said. "It's been coming. We've talked about working better at-bats. We needed to see some pitches and get comfortable and it worked in our favor."
Jordan Henshaw was 2 for 4 with two RBIs to lead the way for the Bruins.
The rubber game of the three-game set is scheduled for 1 p.m. Saturday.