ATLANTA -- Jonathan Dwyer set a school record with an 88-yard touchdown run, Georgia Tech's defense shut out Mississippi State for three quarters and the Yellow Jackets beat Mississippi State 38-7 on Saturday.
Georgia Tech (3-1) ran for 438 yards, its most since 1978 and the fifth-highest total in school history.
Shaw, a freshman who also threw a touchdown pass, took over after starter Josh Nesbitt suffered a hamstring injury on a 21-yard run on Georgia Tech's first drive.
Mississippi State committed four turnovers as its streak without offensive points was extended to eight quarters before a fourth-quarter touchdown. The Bulldogs (1-3) lost 3-2 to Auburn last week.
Cornerback Jahi Word-Daniels had a touchdown-saving play, a fourth-down stop and an interception. Defensive end Michael Johnson blocked a field goal, deflected two passes, recovered a fumble and had a fourth-down sack.
Mississippi State appeared to be on the verge of ending its scoring drought in the second quarter when Anthony Dixon took off from the Bulldogs' 20 on a 71-yard run. Word-Daniels made a diving grab for Dixon's foot, slowing the running back so Morgan Burnett could make the tackle at the Georgia Tech 9.
Four plays later, Johnson blocked Adam Carlson's 18-yard field-goal attempt.
Burnett intercepted a pass by Wesley Carroll at the Georgia Tech 2 to end a 15-play drive by the Bulldogs at the end of the first half.
Mississippi State had another scoring chance end when backup quarterback Tyson Lee was sacked by Johnson on a fourth-down play from the Georgia Tech 7 on the first play of the fourth quarter.
Georgia Tech had backups on the field when the Bulldogs finally scored on a 6-yard run by Robert Elliott midway through the final quarter.
Georgia Tech opened with an 11-play drive -- all running plays -- which ended with a 7-yard scoring run by Peeples. The long drive set the pace as Mississippi State couldn't stop first-year coach Paul Johnson's spread option attack.
Shaw had a 20-yard scoring pass to Demaryius Thomas later in the first quarter and a 25-yard touchdown run in the second period.
Georgia Tech began its first possession of the second half at its 12. Dwyer broke free and, aided by running back Lucas Cox's downfield block on safety Derek Pegues, ran 88 yards for the touchdown.
Before Dwyer's run, the longest run from scrimmage in Georgia Tech history was an 87-yarder by Bob McCoy against The Citadel in 1948.
The announced attendance was 48,402, but few remained when Mississippi State's final possession ended with its final turnover on a fumble by Lee inside the Georgia Tech 10 with 5 seconds left.
Brandon McRae had 10 catches for 102 yards and Dixon rushed for 94 yards for Mississippi State in the first meeting between the teams since 1929.