GAINESVILLE, Fla. (AP) — Southern Mississippi wasn’t even sure it was going to get an invitation to the NCAA tournament. Now, the Golden Eagles are one win away from an even more improbable berth.

Corey Stevens drove in three runs, reliever Jonathan Johnston pitched 3 2-3 scoreless innings and Southern Miss beat Florida 9-7 in an NCAA super regional opener Saturday. The Eagles (39-24), the biggest surprise of the tournament, are one win away from going to their first College World Series.

‘‘It’s incredible,’’ second baseman James Ewing said. ‘‘This has been a storybook end of the year for us. It was kind of a coin flip if we were going to get into the tournament or not. It feels great to get this first win, but we still feel like we haven’t accomplished anything yet.’’

Southern Miss won for the 11th time in its last 14 games, a hot streak that started shortly after coach Corky Palmer announced his retirement.

Just a few weeks ago, the Eagles merely wanted to get Palmer into the NCAA field. But after upsetting Georgia Tech and Elon in the Atlanta regional last weekend and then taking the first game in Gainesville, they’re looking to give him an even bigger send-off.

‘‘It’s definitely a great feeling. It’s always a dream to go to Omaha,’’ center fielder Bo Davis said. ‘‘But just like from the first game on, we’ve been the underdog and we still have that mentality. They’re not going to give us anything. We got to fight just like we did today, every single pitch, never give up. We’ve just got to win one more.’’

The Eagles will get their ace, Todd McInnis, on the mound Sunday, too.

They can only hope he pitches as well Johnston, who deserved much of the credit for the latest victory. He allowed just two baserunners en route to his first win this season. Collin Cargill pitched the ninth for his 12th save.

Florida (42-21) made it interesting, though.

Avery Barnes singled to start the ninth and nearly beat out a fielder’s choice at second, a call coach Kevin O’Sullivan questioned.

The Gators got two more hits in the inning, but sixth-year senior Brandon McArthur grounded out to end the game.

Florida’s biggest problem was taking advantage of favorable situations. The Gators loaded the bases with no outs in the fourth, but followed with a strikeout and an inning-ending double play. They had the same scenario in fifth, but couldn’t break the game open.

Johnston did the rest. He retired the side in order in the seventh and eighth.

‘‘The heroes are really too many to name,’’ Palmer said. ‘‘I can remember so many big hits from different guys. From top to bottom, we did some good things.’’

Ewing had three hits and drove in two runs for the Eagles, whose first four hitters combined for eight hits, two walks, six runs and six RBIs.

Southern Miss scored first on B.A. Vollmuth’s fourth homer of the postseason, a solo shot in the second. But the real damage came a few innings later — after a 59-minute rain delay in the third inning.

The Golden Eagles — who had more than 1,000 fans make the trip to Gainesville — tagged starter Stephen Locke for three runs in the fifth, then roughed up Patrick Keating (4-4) for four more in the sixth.

The Gators couldn’t get the momentum back. They can only hope to even the series Sunday.

‘‘This thing’s not over with yet,’’ O’Sullivan said. ‘‘We’re not out. We’ve had our backs against the wall all year, so this is not something we’re not used to.’’

Southern Miss could say the same thing, especially since this is the furthest the program has been in its history.

‘‘Our goal is to get to Omaha, Neb., and compete for a national championship,’’ Ewing said. ‘‘And we haven’t reached that yet. We’re not up too high yet. We’ve got to go out and get another win.’’