Wolford, who set a school record for a quarterback by starting a season opener for the fourth time, completed 11 of 15 passes for 107 yards and also gained 47 yards on the ground. He was removed before the end of the second quarter, as the Demon Deacons had the game well in hand against their FCS opponent.
His backup, Kendall Hinton, was 7 for 8 for 124 yards and two passing touchdowns plus a rushing touchdown.
The lone bright spot for Presbyterian was freshman Torrance Marable, who rushed 16 times for 162 yards.
Wolford's first touchdown pass went for 8 yards to tight end Cam Serigne just 90 seconds into the Demon Deacons' first possession. Wolford's next scoring pass went for 26 yards to Serigne.
Mike Weaver's 22-yard field goal made it 16-0 in the first quarter.
Wolford ran in from 2 yards in the second quarter before throwing to Greg Dortch for a 7-yard touchdown on the first play after a Presbyterian turnover.
Dortch, a redshirt freshman, then caught a 42-yard touchdown pass from Hinton, and it was 37-0 at the half. Hinton added a 29-yard touchdown pass to Alex Bachman in the third quarter before scoring on a 1-yard keeper.
Freshman running back Mark Robinson put Presbyterian on the board with a 14-yard touchdown run with 8:23 remaining.
This marked Wake Forest's third victory in an opener against Presbyterian since 2010.
Arkeem Byrd was Wake Forest's leading rusher with 75 yards on seven carries.
The Blue Hose had only 53 yards of total offense in the first half.
Presbyterian quarterback Ben Cheek was 2 of 9 for 41 yartds and one interception.
The outcome ruined the return of Bobby Spangler, who began his second stint as Presbyterian's head coach after serving most recently as defensive coordinator. This is his seventh season overall in charge of the Blue Hose.