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The win gave the Tigers their 19th consecutive series win over Ole Miss in Baton Rouge. The Rebels' last series win on LSU's home field came in 1982.
LSU improved to 25-12 overall and 9-6 in SEC games, while Ole Miss dropped to 22-14 overall and 7-8 in conference play.
Freeman secured the win for the Tigers, making an acrobatic leaping grab of a line drive off the bat of Ole Miss leftfielder Bryan Seamster with a runner on second and two outs in the top of the ninth inning.
"I told Cole Freeman not to let anyone ever tell him that he's too short," said LSU coach Paul Mainieri. "I'm glad he's 5-9 and not 5-8, or he wouldn't have been able to make that play. This is SEC baseball, you're competing against great players in every game, and it takes every ounce of everything you've got in order to win."
Walker (5-0) earned the win, allowing two runs on six hits while striking out five and surrendering no walks. Right-hander Hunter Newman pitched the ninth and kept the Rebels off the scoreboard to earn his fifth save of the season.
Ole Miss starter Ryan Rolison (4-2) was charged with the loss, as he surrendered three runs – two earned – on eight hits in 5.2 innings with no walks and five strikeouts.
The Tigers will return to action Tuesday night at 6:30 p.m. CT, when they face Lamar University in Alex Box Stadium, Skip Bertman Field. The game will be available online via SEC Network +, and it can be heard on affiliates of the LSU Sports Radio Network and at www.LSUsports.net/live.
Blackman redeemed himself in the top of the third, leveling the score with a solo home run to left field, his fifth dinger of the season and his third of the series.
Rightfielder Greg Deichmann quickly reclaimed the lead for the Tigers with a solo shot of his own in the bottom of the third, this one landing about seven rows into the Diamond Deck in right field. The homer was Deichmann's 12th of the season and the first allowed this year by Rolison.
Ole Miss threatened with a runner on third and one out in the top of the sixth, but Walker escaped the inning after Freeman snagged a line drive and quickly fired to third to double up the runner.
Ole Miss got the run back in the top of the seventh on an RBI single up the middle from catcher Nick Fortes.
LSU freshman right-hander Zack Hess entered the game in the seventh in relief of Walker and pitched 1.1 scoreless innings with no walks and three strikeouts.