LSU second baseman JaCoby Jones made a diving stab for the ball but couldn't come up with it. Britton was hitting .149 coming in, but wound up getting swarmed by teammates who get to face Kentucky Saturday for a berth in the championship game.
"When I saw (Jones) dive, my stomach kind of dropped because I thought he got it," Britton said. "I just kept running until I saw that the ball got past him. I felt pretty happy about it."
Mitch Slauter drove a one-out double to the center field wall for the Bulldogs (37-22), who had rallied with two runs in the ninth and one in the eighth.
Reliever Nick Rumbelow came in to face Britton, who entered as a pinch-runner in the ninth and scored the tying run off the Tigers (43-16).
He grew up in Cullman, Ala., about an hour away from Regions Park and frequently attended SEC tournaments.
"I always dreamed about playing," Britton said. "When I got the opportunity, it was a big deal to me."
Wes Rea opened the ninth with a double down the right-field line off LSU closer Nick Goody that was just inside the foul line and out of reach of a diving Mason Katz, starting the rally.
"A big game that you seemingly have in hand, and then you can't hold the lead in the ninth inning," LSU coach Paul Mainieri said. "For a long time we were very fortunate to be shutting them out.
"We made some tremendous defensive plays."
Daryl Norris and Adam Frazier both singled and Luis Pollorena, who pinch-ran in the eighth, drove in the tying run with a sacrifice fly to center.
Pollorena has only three at-bats this season.
"There was no doubt in my mind he was going to make contact," Mississippi State coach John Cohen said.
Goody got Hunter Renfroe to pop up to send it to extra innings.
Jonathan Holder (2-0), who hasn't allowed a run in 22 appearances this season, pitched around an error for a scoreless top of the 10th. Holder ran his streak of scoreless innings to 26-1/3 to break Bobby Reed's school record.
He already had two saves in the tournament.
LSU took a 3-0 lead after two innings but couldn't score again.
"Our kids stayed with it and showed great fortitude," Cohen said. "When you get behind 3-0 against a very, very good LSU club, it is easy to say, 'Well, we've got regionals next week and we played well down the stretch.' These kids did not have that attitude."
Click here for more at Inside Mississippi State Sports Blog with Brad Locke. Read more in Saturday's NEMS Daily Journal newspaper.