The Tigers (23-14) rebounded with a run in the top of the ninth when shortstop DJ LeMahieu doubled with one out and scored on designated hitter Taylor Davis' single. However, UNO closer Ryan O'Shea retired centerfielder Leon Landry and second baseman Ryan Schimpf on fly balls to the outfield to end the game.
O'Shea (1-1) earned the win, allowing one run on two hits in 2.1 innings with no walks and two strikeouts. Bradshaw (1-5) was charged with the loss as he surrendered three runs on two hits with two walks and two strikeouts.
"This is a tough loss, because I thought we had opportunities during the game to score and expand our lead," said LSU coach Paul Mainieri. "UNO got a big hit at the right time and they were able to win the ball game. We have to rebound quickly because we have the SEC leader (Georgia) coming to Alex Box on Friday. This is a huge weekend for our team as we move into the stretch run of the season."
UNO (23-12) took a 1-0 lead in the bottom of the first when leftfielder Joey Butler launched a solo homer – his 10th dinger of the season – against LSU starter Austin Ross.
The Tigers tied the game in the second against UNO starter Jake Henderson on an RBI single by centerfielder Leon Landry.
LSU grabbed a 2-1 lead in the fourth when rightfielder Derek Helenihi led off the frame with a double and later scored on first baseman Matt Clark's RBI groundout.
The Tigers extended the lead to 3-1 in the fifth when Landry launched a solo blast, his second homer of the season.
UNO responded with a run in the bottom of the fifth against LSU reliever Ryan Byrd as catcher Josh Vander Hey singled, moved to second on a groundout by designated hitter Jeff Lanning and scored on rightfielder Mark McGonigle's RBI single.
Helenihi led off the sixth with a single against UNO reliever David Burch before he stole second base and moved to third on Vander Hey's throwing error. Helenihi later scored on shortstop DJ LeMahieu's single to right field, giving the Tigers a 4-2 lead.
UNO narrowed the deficit to 4-3 in the bottom of the sixth when Butler singled, moved to third on a single by third baseman T.J. Baxter and scored when reliever Paul Bertuccini fired a wild pitch.
LSU resumes Southeastern Conference action at 7 p.m. on Friday when the Tigers play host to Georgia in Alex Box Stadium.