Laxer (4-0) worked a career-best seven innings, allowing four hits with a walk and five strikeouts. R.J. Hively picked up his second save of the season, working the final inning with two strikeouts and retiring the side.
"I'm proud of Josh," said Ole Miss head coach Mike Bianco. "I thought he was special tonight."
It was the seventh shutout victory of the season for the Rebels (29-16), who played errorless ball.
"We played great defense," Bianco said. "We normally play well defensively, but tonight we had a couple of web gems and in this type of game, those plays can be game changers."
Will Allen singled home Matt Snyder, then scored himself on an infield hit by John Gatlin (Tupelo) for a 2-0 lead in the first inning. Allen scored in the fourth on a sac fly by Auston Bousfield.
Allen and Gatlin each went 2 for 4 to lead a seven-hit attack.
Junior lefty Dillon Day (0-1) suffered the loss for Southern Miss (25-19) in his first pitching appearance of the season, allowing three runs - two earned - on six hits with a walk and three strikeouts in five innings of work.
Ole Miss is home tonight at 6:30 against Murray State. Fourth-ranked LSU visits this weekend.
The loss snapped a three-game winning streak for Southern Miss against the Rebels. The Golden Eagles will be home tonight against Grambling.