LSU started off the day by winning Friday's suspended game one in the 12th inning on a Mason Katz RBI single. But the Seawolves recovered take game two and forced a deciding game three on Sunday afternoon.
Johnson (12-1) picked up his third win of this postseason and allowed just an unearned run. Sophomore Kevin Courtney led the Seawolves with three hits and an RBI in addition to scoring two runs.
Courtney has five hits in eight at-bats through two games of this Super Regional.
LSU right-hander Kevin Gausman, who was drafted No. 4 overall in the MLB draft earlier this week and picked up the win game one, took the loss as he allowed three runs on seven hits in 7.0 innings.
Stony Brook again jumped to early lead, scoring two runs in the third on RBI singles from senior Sal Intagliata and junior William Carmona.
Johnson did not allow a hit to the fifth when Jordy Snikeris led off with a single to right. Tyler Moore drew a walk with Snikeris going on the pitch and Snikeris was then ruled out by the umpires after sliding past second.
Johnson then got the next two hitters on groundouts to get out of the jam. Courtney pushed the Seawolves lead to 3-0 in the bottom of the fifth, homering to right to lead off the inning.
LSU got on the board with an unearned run in the sixth and had runners on first and second with one out. But Johnson got Snikeris to ground into a 6-4-3 inning ending double play.
Johnson cruised from there, retiring the next eighth hitters before Snikeris reached on an error with two outs in the ninth. But Johnson got Tyler Moore to pop up the third to end it.