The 17 strikeouts by Alabama hitters was an SEC Tournament record. Nine different batters struck out at least once for Alabama.
Even with the futility at the plate for most of the night, it was a game the Alabama squad might have won without base running mishaps and one error-plagued inning.
Alabama squandered opportunities to score in the first and second innings, and made three fielding errors in the second inning that allowed Mississippi two runs.
Leadoff man Emeel Salem drew a walk and advanced two bases to third when Holliman threw the ball away trying to pick Salem off.
Ole Miss third baseman Clay Goodwin later cut down Salem at the plate as he was trying to score on a Gabe Scott chopper, however.
Morrow Thomley doubled to left-center field to lead off the second inning, but he was picked off after he strayed too far from the bag for the first out of the inning.
"Those things are so evident when you have so few opportunities," Alabama Head Coach Jim Wells said.
Holliman (7-3) pitched seven innings and allowed four hits and no runs. He walked four batters to go with his 14 strikeouts.
"We had chances early in the game, but when a guy pitches that good he deserves to win," Wells said. "To keep it simple (Holliman) was just that dominant. Early in the game he was up in the zone. Our only hope was that he walk us and somebody hit one."
While squandering its own chances, the Tide defense failed in the second inning with three costly errors. Second-baseman Greg Paiml committed the first error of the inning in trying to double up Ole Miss's Mark Wright. His throw went into the camera well allowing him to advance to second base.
Wright later scored on a Zack Cozart single when Emeel Salem's perfect throw from center field was mishandled by catcher Kody Valverde.
Wade LeBlanc, who was backing up on the play, tried to throw Cozart out at third, but launched the ball over Bush's head, allowing Cozart to cross the plate.
Salem was charged with a throwing error on the play, even though his perfect one-hop throw to the plate was missed by Valverde.
Alabama, who was the visitor in the game, had a chance right at the start of the game, which was an hour and 52 minutes late due to a marathon game played between Florida and Arkansas.
Stephen Head pitched the final two innings, allowing a run on two hits while striking out three batters.
The Crimson Tide got the tying run on first base when Rocky Scelfo singled in the ninth driving in Thomley, who had singled to lead off the inning.
The loss overshadowed a remarkable performance by LeBlanc. He threw a complete game, allowing six hits and just one earned run in the game. LeBlanc walked just one batter and struck out five.
"LeBlanc pitched well for us and that gave us a chance," Wells said.
Emeel Salem was the only Alabama batter that did not strike out on Wednesday evening. Evan Bush and Zac Welch each had a hat trick, going down on strikes three times.
Bush struck out looking to end the Tide's half of the eighth inning, and was ejected for arguing with home plate umpire Jack Cox.
Cox expanded the strike zone in the ninth inning as a result, ringing Zac Welch up on wide strike.
Alabama will face Arkansas at 1 p.m. Thursday afternoon and will start either Trey Shields or T.J. Large. Arkansas will start Charley Boyce, who beat Alabama twice in Tuscaloosa less than two weeks ago.
The session II attendance for the tournament was 11,318.