Dundrecous Nelson added a career-high 16 points for the Rebels. Chris Warren added 15 points and Terrance Henry 10.
Ole Miss out-rebounded Saint Louis 42-23, making it three straight games for the Rebels to attain the edge in boards. Graham had a game-high eight boards, while Demarco Cox, making his second career start, grabbed seven.
Ole Miss made 25 of its 29 free throws, many of which sealed the win down the stretch.
"Since we've been in this country, we've made free throws and we've rebounded the ball," head coach Andy Kennedy said. "Unfortunately from behind the arc we have left a lot to be desired, and it's the reason we were not playing in the (championship) game. But we salvaged our season by getting this win."
The Rebels led 28-24 at the half, despite shooting just 36.7 percent in the first half.
Saint Louis (5-7) was led by Kyle Cassity's 21 points and Brian Conklin's 19. Both players were instrumental in a late second-half run that brought the game back to within reach for the Billikens.
"This was a good win for us, under the circumstances," Kennedy said. "We basically played without two of our top four players. Reginald Buckner was a non-factor, fouled out in 11 minutes. And obviously without Trevor Gaskins (hamstring injury), we're digging deep. We're asking Steadman Short and Demarco Cox to play much heavier minutes. I thought they responded. Chris (Warren) has been in a funk shooting the ball. Unfortunately that continued for him from 3. But he continues to be good at the free throw line."
Kennedy felt Nelson was outstanding.
"I thought he was tremendous," he said of the freshman from Jackson. "He's a very talented player, made big shots, made good decisions. I thought he defended very well."
Nelson said his mindset was to do whatever it took to help obtain a victory.
"This was a good win. We let the last game slip away from us," Nelson said of Thursday night's loss to Colorado State. "Coach challenged everybody on the whole team to make a push today and get this win."
Billiken head coach Rick Majerus did not coach from the sidelines due to an illness he developed while in Cancun.
"We get a little break now for a few days," Kennedy said, "regroup, and get back at it."
Ole Miss will be back in action Thursday with a home game against Alcorn State. Tipoff is 7 p.m. at Tad Smith Coliseum, and the game will be televised by FOX Sports South.