Against the Orangemen, Godsey hooked up with record-setting Kelly Campbell 10 times for 193 yards and Joe Burns ran for 113 yards and a touchdown in the lowest-scoring Kickoff Classic ever. In '86, Alabama beat Ohio State 16-10.
Godsey, who completed 64 percent of his passes last season, was 15-of-26 for 224 yards, and cornerback Marvious Hester intercepted a pass at the Syracuse 6 to set up Burns' 1-yard TD with 8:27 left in the half for a 10-0 lead.
Luke Manget had field goals of 22 and 20 yards - one in each half.
Campbell broke the school record for receiving yards on a 72-yard hookup with Godsey early in the second quarter. The reception pushed him past Harvey Middleton, who had 2,291 yards from 1994-97. Campbell now has 2,392 yards.
The catch was also the longest in Kickoff Classic history, topping the 67-yarder from Miami's Kenny Kelly to Santana Moss in 1999.
"They were letting me open underneath, something we didn't expect," Campbell said. "I was kind of surprised. We figured they were going to double up on me with the safety, but I think the coaches just wanted to continue to get beat on down the field."
Burns was a workhorse, carrying a Kickoff Classic-record tying 34 times. He gained 55 of his 113 yards on three runs late in the game.
Syracuse, guilty of crucial penalties that kept alive Georgia Tech drives, stayed in the game thanks to the Yellow Jackets' failure to make big plays.
Troy Nunes, sacked three times and twice knocked out of the game for a brief spell, scored on a 1-yard keeper with 8:35 left in the third quarter to pull the Orangemen within 10-7. But the Yellow Jackets defense - helped by several tipped passes and a dropped ball by Johnny Morant at the Tech 24 with 6:32 left - held on.
Nunes finished 19-of-32 for 183 yards and an interception.
"I think Georgia Tech came in sleeping a little bit," said Syracuse wide receiver David Tyree, who had seven catches for 67 yards. "The major thing is we just have to finish our drives. We were pretty much able to win the game but we just didn't convert."
Tech, which finished last season averaging almost 34 points and 435 yards per game, had 349 total yards, while holding Syracuse to 242.
The game at Giants Stadium drew the smallest crowd in 19 Kickoff Classics at 41,517. The '92 game between North Carolina State and Iowa drew 46,251.
Tech led 3-0 when Campbell made his record catch, but couldn't score on four running plays from the 8-yard line. On fourth-and-3, Burns, being pushed forward by Godsey, was stopped at the 1 by cornerback LaTroy Oliver.
Syracuse gave the ball back three plays later when Nunes' pass was intercepted by Hester and returned 10 yards to the Orange 6. Tech nearly blew another scoring chance, but Syracuse was called for holding on a third-down play from the 5 and the Yellow Jackets had another first down at the 2. On fourth down, Burns scored.
Manget made his 92nd consecutive extra point - one shy of the ACC record - but only after getting a second chance. He missed his first try, but kicked again when Syracuse was penalized for too many men on the field.
Mike Shafer was wide right with a 26-yard field goal attempt for Syracuse with 3:12 left in the first quarter.