The Panthers trailed 4-1 before rallying with two runs in the sixth and then two more in the seventh to win their second straight and improve to 6-4. Boston College fell to 1-6.
Burns (2-1), the junior left-hander, relieved starter Nick Squeglia in the third inning and allowed just one run on three hits with five strikeouts over the final seven frames. Sarratt, the senior catcher, had three hits and two RBI.
"What a great team win. This is the way Friday night baseball is supposed to be played," said GSU head coach Greg Frady. "Boston College had the momentum early and all the breaks were going their way, but we stayed calm, battled through tough situations and executed.
"Ben Burns was masterful," Frady continued. "He was in control the whole way, and Boston College never got many good swings on him. And Scott Sarratt came through with two huge hits. He left it all out there tonight."
Trailing 4-1, the Panthers pushed across two runs in the sixth. Mark Hogan led off the inning with a single, and then Nic Wilson walked. After a groundout put the runners at second and third with one out, Sarratt singled home Hogan. With two outs, Caden Bailey's opposite field single scored Wilson and pulled the Panthers within 4-3. Bailey extended his hitting streak to 13 games.
Chris Triplett followed with an infield single to load the bases with, and it appeared GSU might take the lead when Josh Merrigan drove the ball deep to left field, but BC's Logan Hoggarth made the catch as he fell down.
One inning later, freshman Matt Rose led off the seventh with a walk, stole second and then moved to third on Hogan's groundout to the right side. Wilson hit a fly ball to right field to bring Rose home with the tying run.
After Chase Raffield's two-out single, Sarratt drilled a double over the left fielder's head to plate the go-ahead run.
After allowing a run in the sixth inning on a bad-hop single, Burns induced a double play and retired the final eight batters in a row.
"I got ground balls, and my fielders made plays behind me," said Burns. "We just did all the little things. We're never out of the game with out offense. Definitely a big team win tonight."
After falling behind 3-0 early, Georgia State got on the board in the third as Rose crushed a double over the center fielder's head to score Merrigan, who singled with two outs. Merrigan had three hits on the day.
"We didn't start the game the way we wanted to, but we minimized the damage," said Sarratt. "Ben came out of the bullpen and did and amazing job. Then we just kept chipping away."
Boston College starter Eric Stevens allowed three runs on 11 hits in 5-2/3 innings but did not figure in the decision. Hunter Gordon (0-1) took the loss for the Eagles.
The series continues with game two set for Saturday at 7 p.m. at Al Lang Stadium.