Northwestern (6-5), which opened a stretch of five home games in four days, stranded nine runners, five in scoring position, including leaving the bases loaded without getting on the board in the second inning.
LSU (11-2) pushed across single runs in the first and third innings despite getting only two hits off Demons starter Steven Spann (2-2).
The Tigers added two more in the fourth without benefit of a hit or an error, and finally got the bats moving in the final five innings, collecting eight of their 10 hits.
The Demons had five hits and stranded six runners in the first four innings. They got their only run in the fourth, closing the gap to 4-1 on a sacrifice fly by Nathan Lyons to score Chase Daughdrill, who had a one-out single and moved around to third on an Edwin Gomez base hit.
"We give up two leadoff walks and they came around to score, and we load the bases in the second inning and we don't scratch.
That's the difference," said second-year Demons' coach Lane Burroughs. "You have to find a way to get on the board, and it may be a different game. It's going to come back to haunt you, especially against a really good team like LSU."
The Tigers broke it open in the sixth in the second inning of work by Josh Morris, who was touched up for four hits in the inning.
LSU manufactured its fifth run off a steal following the game's first extra-base hit, a double by Christian Ibarra, followed by a base hit from Andrew Stevenson, who swiped second after getting caught in a rundown that allowed Ibarra to scamper home.
Moore followed with a homer over the right-field wall for a 7-1 lead.
"Some young pitchers got in and we left some balls up, and we saw what happens against good hitters when you do that," said Burroughs.
Gomez had a pair of hits for NSU, which didn't have any for extra bases and was hitless in the final four innings.
"We took some good swings, we barreled some balls, but overall offensively, we have to get runs in when the opportunity presents itself," said Burroughs. "Once we got behind by a bigger margin, our approach had to change. You have to go station-to-station, you need to take, and make their freshman throw strikes. You're not in the same mode as you are in a tight game or you're ahead. But credit to their guys, they found a way to shove it in the zone and get the job done."
NSU's defensive performance was highlighted by a couple of nifty plays at third base by Daughdrill.
"We did play good defense. Chase Daughdrill made a couple of really good plays at third that prevented a lot of damage," said Burroughs.
Burroughs and his team were appreciative of the turnout for the game, which began in cloudy and crisp conditions after a steady rain fell overnight and in the early morning.
It was the third-largest crowd in Brown-Stroud's long history.
"You'd like to win this game, a big game, and we had chances to get going early. We appreciate everybody coming out. To be the elite program we want to be, where we're heading, you have to find a way to cash in when it presents itself, and we didn't do that today."
NSU plays Friday night at 6:30 against Chicago State, and will play two times Saturday against McNeese State (noon) and Chicago State (6:30), before wrapping up the weekend Sunday at 4:30 against the Cowboys at Brown-Stroud Field.