"Defensively, we really got after it," Southern Miss coach Larry Fedora said. "Offensively we had a frustrating night, but we never had to punt."
Southern Miss quarterback Martevious Young made his third start his most consistent, going 13 of 15 for 127 yards with touchdown passes of 21 and 6 yards to Brown, who had four catches for 41 yards.
Green Wave quarterback Ryan Griffin was sacked six times and fumbled twice in his debut as a starter.
Jamie Collins scooped up one of Griffin's fumbles and returned it 15 yards for a touchdown in the second quarter and Andre Watson returned a blocked field goal 77 yards for another score.
The Golden Eagles (5-3, 3-1 Conference USA) held Tulane (2-5, 0-4) to 208 yards of total offense.
Southern Miss defensive tackle Terrance Conner, who wasn't in the starting lineup until Saturday, sacked Griffin three times.
"This is the best performance we've had as a unit," Conner said. "When you force four turnovers you must be doing something right."
Andre Anderson rushed for 92 yards and scored Tulane's lone touchdown in the third quarter.
"It's just devastating going out there and things don't go your way," Anderson said. "You get blocked field goals, fumbles, it's definitely frustrating. This is one of the hardest losses I've ever had."
Fedora said he knew if his defense could stop Anderson, it would put his team in good position to win.
"We held him and (receiver Jeremy) Williams under 100 yards," Fedora said. "That was our goal and I'm proud of our guys for rising to the challenge."