The game was played before a Baum Stadium-record crowd of 10,147, breaking the previous mark of 10,027 set in the 2004 NCAA Super Regional versus Florida State.
LSU improved to 27-20-1 overall and 10-11-1 in the Southeastern Conference. Arkansas dropped to 35-13 and 15-7.
The Tigers moved into fourth place in the SEC Western Division and into seventh place in the overall league standings.
LSU and Arkansas meet in Game 2 of the series at 3:07 p.m. Saturday. Junior left-hander Charlie Furbush (3-6, 5.14 ERA) will start on the mound for the Tigers while Arkansas will counter with junior right-hander Jess Todd (6-2, 3.53 ERA).
"It was a tremendous victory tonight for the Tigers," said LSU coach Paul Mainieri. "We got several clutch hits, and we made some great plays on defense. I thought our pitching was excellent – our guys did an excellent job of keeping their hitters off-balance.
"This is a big win, but it's just one game. We have to continue to play with great intensity and focus against a great Arkansas club in a great venue for college baseball."
With one out in the top of the ninth inning, LSU designated hitter Nicholas Pontiff singled against Arkansas reliever Travis Hill. Chris McGhee, running for Pontiff at first base, then advanced to second on a wild pitch from Hill.
Jackson lined a single into center field, scoring McGhee with the go-ahead run.
LSU reliever Jared Bradford retired the Razorbacks in order in the bottom of the ninth to preserve the win. Bradford improved to 9-2 on the year as he allowed two runs on three hits in three innings in relief of starter Ryan Byrd.
Byrd was magnificent through six innings, limiting Arkansas to two unearned runs on two hits with two walks and four strikeouts.
Hill (3-2) was charged with the loss as he surrendered one run on two hits in 1.2 innings with no walks and three strikeouts.
LSU struck for three runs in the second inning against Arkansas ace Nick Schmidt to take an early lead. Pontiff singled in a run before second baseman Jackson delivered a two-run double to highlight the uprising.
Jackson finished 3-for-4 on the night with three RBI and one run scored while Pontiff was 3-for-4 with one RBI and two runs scored.
Arkansas responded with three unearned runs in the bottom of the third inning as LSU committed three errors in the frame. Leftfielder Casey Coon's two-run single after the third LSU miscue narrowed the gap to 3-2.
LSU held the one-run lead until the seventh inning, when the Tigers added a pair of runs on leftfielder Blake Dean's two-out, two-run single.
Arkansas, however, struck for three runs against Bradford in the bottom of the frame. Bradford gave up a two-out single and hit two batters to load the bases. Coon then belted a bases-clearing double into right-center field to tie the game at 5-5.
Schmidt allowed five runs on eight hits in his seven-inning outing with two walks and eight strikeouts.
Tigers take down No. 3 Hawgs 6-5
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