Tankersley (5-0) went the distance for his first career complete game, holding the Tigers to two runs and eight hits over nine innings. He walked only one batter and added eight strikeouts as he continues to share the SEC lead with Vandy's Jeremy Sowers with 59 strikeouts.
The Vicksburg, Miss., native allowed single runs in the third and fourth innings before settling down to retire the next 10 batters over the next four innings.
After stranding the tying run at third base in a shaky eighth inning, Tankersley finished the game in the ninth with two strikeouts and a line out by Matt Liuzza to shortstop Adam Pavkovich to end the game.
"Both pitchers pitched well tonight," Alabama coach Jim Wells said. "Taylor Tankersley was excellent and pitched the best game of his career tonight. (Wilson) was very good, too. It was a hard-fought game and a pitch-by-pitch game. This was a great college baseball game tonight."
Alabama (20-5, 5-2 SEC) snapped an eight-game losing streak to the Tigers with the win. Prior to Friday, UA had not beaten LSU since May 14, 2000 in Baton Rouge.
LSU right-hander Brian Wilson (5-3) was equally impressive shutting out Alabama over 7 1/3 innings after allowing a three-run home run to Beau Hearod in the first inning.
Wilson was charged with four runs and seven hits in 7 2/3 innings, adding four walks and two strikeouts.
Hearod, a native of Jennings, La., ripped an 0-1 fastball to left-center field in the bottom of the first inning to stake the Crimson Tide a 3-0 lead.
Travis Garner drew a leadoff walk and moved to second base on Allen Rice's sacrifce bunt. Adam Pavkovich then reached on a slow-rolling infield single to second base.
The three-run home run was Hearod's 10th of the season, moving him one ahead of Florida's C.J. Smith for the league home run lead.
LSU (16-9-1, 5-1-1 SEC) scored single runs in the third and fourth innings, but could never tie the game against the ace left-hander.
Jon Zeringue's fourth home run of the season cut the Alabama lead to 3-1 in the top of the third inning.
The Tigers could have made it a one-run game, but missed out on a scoring opportunity after Zeringue's home run. Bruce Sprowl ripped a ball into right center field and appeared to be headed for a one-out triple, but stumbled coming around second base and scrambled back safely.
Ryan Patterson followed with a base hit to right field and Hearod's strong throw beat Sprowl to the plate for the second out of the inning, ending the LSU threat.
LSU cut the lead to 3-2 in the fourth inning when Blake Gill drew a lead off walk and then moved to third on Clay Harris' double into the left field corner. Quinn Stewart lifted a sacrifice fly to center field and Gill slid across the plate just ahead of Garner's throw home.
Both teams had other chances to score, but the pitching and defense held the other team's offense in check.
Both teams also played errorless baseball.
Alabama stranded eight base runners, including runners at third base in the third, seventh and eighth innings. LSU left seven base runners and stranded the tying run at third base in the eight inning when Gill lined out to Pavkovich to end the inning.
Alabama got a much-needed insurance run in the bottom of the eighth inning, chasing Wilson with two outs. Wilson walked Zac Welch and Nathan Meiners, before getting a ground out of pinch-hitter Spencer Pennington for the second out.
Jake Tompkins came in from the bullpen and gave up a two-out single to pinch-hitter Ryan Beagle, making just his third plate appearance of the season. Beagle singled to right field to score Welch and give the Crimson Tide a 4-2 lead.
After allowing a leadoff single in the ninth, Tankersley recorded back-to-back strikeouts before getting Liuzza to line out to end the game.
Hearod was the only UA player with two hits in the game. Garner extended his hitting streak to 15 games with a fourth inning single.
Harris had three hits for LSU, including a pair of doubles. Patterson also added two singles for the Tigers.
The second game of this three-game series is set for 4 p.m. Saturday afternoon following the Crimson Tide football team's annual A-Day game at Bryant-Denny Stadium. Sophomore left-hander Brent Carter (4-2, 2.47 ERA) will take the mound for Alabama, while LSU will counter with right-hander Bo Pettit (4-0, 2.32 ERA).