The Golden Eagles (17-4, 1-0) won for the sixth consecutive time over the Green Wave dating back to the 2009 C-USA tournament.
McInnis (5-1) limited the Green Wave (17-4) to two runs, one earned, over seven innings and scattered six hits and four walks, while fanning five to become the school's all-time win leader with 30. The senior from Brandon surpassed Darrell Lindsey who tallied 29 from 1985-88.
Kameron Brunty, Tyler Koelling and Adam Doleac drove in three runs apiece as the Golden Eagles collected 11 hits in the game. It was the third time in four games Southern Miss has posted 10 or more hits.
The Golden Eagles chased Tulane's Conrad Flynn (2-3) in the third.
The teams return to action today in a 2 p.m., contest. Southern Miss will send righthander Jonathan Thompson (2-0, 4.43 ERA) to the mound against righty Kyle McKenzie (2-2, 3.43 ERA).