Howard (7-6) retired 15 straight for the Eagles (40-21) during one stretch. The left-hander walked two and threw 137 pitches.
Dalton Busby went 3-for-3 with a two-run homer and a double, and Garrett Chapman had a solo home run and a double as Georgia Southern pounded out 16 hits.
Florida State (43-16) had won 19 straight NCAA regional games.
Georgia Southern will play Kennesaw State today, while the Seminoles will play Alabama in an elimination game.
Florida State had as many hits as it did errors.
Georgia Southern chased right-hander Mike Compton (7-3) in the second inning, and the Seminoles used four relievers to finish the game.
Weather wipes out Oxford Regional: Both games in the Oxford, Miss., regional were rained out Friday.
The two games were pushed to today. No. 2 seed Washington will face No. 3 Georgia Tech at 2 p.m., followed by No. 1 Mississippi and No. 4 Jacksonville State at 6 p.m.
The regional will now have three games scheduled for Sunday, with the championship moved to Monday.
Soggy weather could be a threat throughout the weekend, with scattered storms expected throughout the next three days.
Jackson St. 1, Louisiana-Lafayette 0: Vincent Anthonia and Alexander Juday combined on an eight-hit shutout as Jackson State won its first NCAA tournament game, stunning Louisiana-Lafayette.
Desmond Russell doubled and Melvin Rodriguez, who had two of Jackson State’s four hits, drove him in with a single in the fourth to put Jackson State (32-23) up 1-0.
It held up as Anthonia (4-0) threw six scoreless innings and Juday struck out two in his three innings for his third save.
Jackson State, which was 0-10 in regional games, will play Mississippi State tonight. It also was the first time since beating Texas Southern in 1981 that the Lions won a game 1-0.
Louisiana-Lafayette (53-8), ranked No. 1 in some national polls and the No. 6 national seed, stranded 11 baserunners.
Austin Robichaux (7-3) took the loss for Louisiana-Lafayette, which will play San Diego State in an elimination game today.