McInnis, Conference USA's pitcher of the year, set the school record for career innings pitched during the game. He navigated through the first six innings untouched before giving up his only run in the seventh.
He struck out eight in a memorable performance at Trustmark Park, which is just a few miles from his hometown in Brandon, Miss. McInnis (8-2) said about 150 family and friends came to watch the game.
"He earned every bit of it," Southern Miss coach Scott Berry said. "There will be a lot of people in this conference who are happy they don't have to face him anymore."
Southern Miss (39-15) sent 11 batters to the plate during a five-run first inning and cruised the rest of the way. Seven of the first eight batters reached base safely, chasing Tulane starter Conrad Flynn (3-7) before he could record a second out.
"Getting a lead like that just gave me the liberty to throw the ball down the middle and let my defense work," McInnis said.
Issac Rodriguez had a two-run single during the Golden Eagles' decisive first-inning rally. Five different Southern Miss had at least two hits, including Adam Doleac, who finished 3-for-4 and an RBI.
Tulane (30-25) managed just four hits. Reliever Drew Zizinia gave up one run in 6.2 innings of relief.