Zenon had a 19-yard touchdown run in the second quarter -- the first of 24 consecutive points by the Yellow Jackets -- and a 2-yard scoring run in the third quarter.
Byerly, the Yellow Jackets' short-yardage quarterback, had 1-yard touchdown runs in the first and fourth quarters.
The other Georgia Tech touchdown came on a 10-yard interception return by linebacker Quayshawn Nealy in the second quarter.
Georgia Tech (2-0) rushed for 342 yards and converted on 10 of 12 third downs.
Miscues by Tulane (0-2) set up four of Tech's five touchdowns -- three interceptions of Tulane redshirt freshman quarterback Tanner Lee and a blocked punt in the fourth quarter.
A sellout crowd of 30,000 witnessed the first game in Tulane's Yulman Stadium. Saturday's game was the first on-campus home game for Tulane since 1974, a year before the Superdome opened.
The Tulane fans had plenty to cheer early. On the first play from scrimmage, Tulane linebacker Eric Thomas sacked Georgia Tech quarterback Justin Thomas and forced a fumble, which defensive end Royce LaFrance scooped and return to the 8-yard line.
Three plays later, Lee found Justyn Shackleford for a 12-yard touchdown to give the Green Wave a 7-0 lead with just 88 seconds elapsed.
Tech responded with a 10-play, 75-yard drive, using all of the ground elements of its triple-option attack. Byerly came in for the first time on third-and-goal and covered the final yard to tie the game at 7-7.
The Green Wave regained the lead on the next possession with a 75-yard drive of its own, capped by a 24-yard end around by freshman wide receiver Teddy Veal.
The Jackets got even again when Nealy stepped in front of a Lee pass and returned it for a touchdown to make it 14-14 with 11:10 left in the second quarter.
Lee and the Green Wave offense answered quickly with a deep slant to Xavier Rush, who outran the Georgia Tech secondary for a 61-yard touchdown to give Tulane a 21-14 lead with 9:38 left in the half.
Georgia Tech's second interception of Lee -- by Demond Smith -- set up another tying touchdown. Zenon raced around left end for a 19-yard score with 2:51 left in the half to make it a 21-21 game.
Tech took its first lead of the day, 24-21, on a 46-yard field goal by Harrison Butker as time expired in the half, moments after a failed fourth-down try by Tulane.
Tulane got the ball to start the third quarter, but Lee's third interception -- this time by Lawrence Austin -- set up a 76-yard, 12-play drive by the Jackets that took 6:42 off the clock, capped by Zenon's second score.
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