Harris, who went to left field with both of his shots, put LSU ahead 7-5 in the seventh inning with his second blast of the day and third of the season. Third baseman Wally Pontiff provided what would be the winning run in the eighth with a two-out RBI double.
ULM used back-to-back doubles to plate two runs in the top of the ninth, but LSU closer Brian Wilson held on to earn his second save of the series.
The first homer from Harris, which easily cleared the left field bleachers, put LSU ahead 4-3 in the third inning. ULM rebounded for two runs in the fifth, and LSU tied the game with a two-out RBI single from shortstop J.C. Holt in the sixth.
After Pontiff drew a leadoff walk in the seventh, Harris cleared the fences on a 1-2 pitch from ULM reliever Michael Lovelace – the third of four pitchers the Indians used in the game.
LSU (13-5) also threw four pitchers on the day, and the second for each team went down as the pitcher of record.
Brad David (W, 2-1), a fifth-inning replacement for starter Lukas Guidroz, held the Indians to one run on four hits over three innings. Weylin Guidry got the final two outs of the eighth inning, and Wilson lasted through two hits and walk in the ninth.
Lee Graves (L, 1-2) who came into the game for ULM starter Matt Guillory in the third inning after Guillory served up the first homer to Harris.
Although ULM (5-11) didn't get any home runs, they totaled a season high 15 hits against LSU pitching, including five doubles. The Indians failed to take advantage of many of their opportunities, however, hitting into three double plays and getting two batters picked off on the base paths.
The double plays were indicative of the solid defense LSU played throughout the series. The Tigers first error of the weekend came in Sunday's game, a throwing mistake from Holt to lead off the sixth inning. But the freshman redeemed himself later in the inning by starting a 6-4-3 double play to retire the side.
A wild pitch in the first inning turned what should have been a strikeout into a one-out opportunity for Louisiana-Monroe. Guidroz got third baseman Ted White to swing at strike three but the wild pitch went to the backstop and allowed White to reach first.
After retiring, designated hitter Jason Lind with a strikeout looking, Guirdoz got centerfielder Cade Eady to hit a soft grounder to the right side. LSU first baseman Jason Columbus cut off the ball before it got to the outfield but couldn't position himself for a clean throw to Guidroz covering first.
Eady was awarded an infield single and scored along with White when catcher Joey Wolfe laced a double over the bag at third base. ULM second baseman Jack Skaggs followed with a single to deep second that Blake Gill got in his glove but couldn't get in first in time for the third out. Wolfe was running the entire time and reached home for a 3-0 Indians' lead.
LSU got on the scoreboard in the second inning with back-to-back doubles with one out from left fielder Matt Heath and Columbus. Heath sent his to deep right center and the wind played with Columbus' shot to center, sending Heath home and leaving Eady guessing where the ball would go. Columbus scored when Holt hit a two-out single to left field
Wolfe had a chance to extend ULM's lead in the third with runners on first and third with one out, but he hit into a 5-4-3 double play.
As he would in the seventh inning, Pontiff started the third with a base on balls. The Indians issued three free passes to Pontiff on the afternoon, and it wasn't until he got the game-winning hit in the eighth that he extended his hitting streak to ten games.
Harris accepted the first offering from Guillory, a fastball, and deposited it deep in the left field parking lot for LSU's first lead in the game.
One-out singles from right fielder Jaime Estrada and White in the fifth inning ended the day for Guidroz. He left having given up four runs on eight hits and two walks with two strikeouts.
Estrada scored from third base after David took the mound when White got hung up in a rundown between first and second. Designated hitter Jason Lind then greeted David with a single to center field, and Eady followed with an RBI double down the left field line to put the Indians ahead 5-4.
With Sunday's win over Louisiana-Monroe, LSU has earned three weekend sweeps in 2002. Vanderbilt comes to Alex Box for the Tigers' next opportunity, following a Tuesday contest with Louisiana-Lafayette.