The Tigers improved to 7-2 with the victory, while McNeese dropped to 2-6. LSU opens a three-game series with Dartmouth at 7 p.m. Friday at Alex Box Stadium.
Katz, who has reached base in 12 consecutive plate appearances, produced a three-run homer and a double to pace the Tigers' 16-hit attack.
Third baseman Tyler Hanover added 3 hits, including two doubles, and drove in 4 runs for the Tigers while right fielder Raph Rhymes was 2-for-2 with 2 RBIs.
"Obviously, I like the way we're swinging the bats right now," LSU coach Paul Mainieri said. "Mason Katz is on fire right now, and we're getting good at-bats throughout the lineup."
Freshman right-hander Aaron Nola (1-0) earned the win in his first collegiate start, working 5 innings and limiting the Cowboys to three runs on six hits with one walk and 6 strikeouts.
"I was very proud of the way Aaron pitched tonight in a new environment," Mainieri said. "He showed a lot of poise and gave us the outing we needed to win this game."
McNeese State starter Caleb Miller (1-2), the first of eight Cowboy pitchers, was charged with the loss as he allowed nine runs on eight hits in 6.1 innings with four walks and three strikeouts.
LSU grabbed a 2-0 lead in the top of the first inning against McNeese starter Caleb Miller as Rhymes delivered an RBI single and shortstop Austin Nola produced a run-scoring groundout.
The Tigers expanded the lead to 5-0 in the second when Katz launched a three-run homer, his first dinger of the year.
McNeese State struck for three runs in the fifth against Nola as center fielder Andrew Guillotte ripped a two-run double and catcher Renny Weber added an RBI groundout.
The Cowboys added a run in the sixth to narrow the deficit to 5-4 before LSU exploded for five runs in the seventh to take control of the game. Hanover's two-RBI double highlighted the rally, which gave the Tigers a comfortable 10-4 lead.
LSU added eight runs in the ninth inning against five different McNeese pitchers. Hanover and pinch hitter Evan Powell each ripped two-run doubles to pace the uprising.