Aundrae Allison had eight catches for 158 yards and two touchdowns for the Pirates (1-1), who suffered their first loss under new coach Skip Holtz. Chris Johnson also ran for 102 yards and a score.
The Demon Deacons came into the season saying this was their most talented team under Grobe, but they had yet to show it. They lost their opener to Vanderbilt 24-20 - their seventh loss by seven or fewer points dating to last season - and followed with a 31-3 loss at Nebraska last week.
On Saturday, however, the Demon Deacons finally looked something like the team they claimed to be. Barclay and Andrews led the team's 407-yard rushing total, the school's best rushing day since tallying 528 yards against Tulsa in 1971. Wake Forest took a 31-6 late in the first half and held a 21-point lead midway through the third quarter before the Pirates fought back. Johnson capped a 64-yard drive with a 12-yard score, while Allison broke free from a defender for a 59-yard TD pass from James Pinkney that made it 34-27 at the end of the third quarter.
But the Demon Deacons - behind their impressive rushing tandem - put the game away with a pair of scoring drives.
On the first, Andrews cracked the 100-yard mark with a 44-yard sprint to the 15, setting up Sam Swank's 30-yard field goal for a 37-27 lead with 12:13 left.
Then, after East Carolina went three-and-out, Barclay took a third-down carry straight up the middle and broke free for a 65-yard score and a 44-27 lead with 9:35 left.
Barclay's big day - his second career 200-yard effort - was a welcome sight for the Demon Deacons. The two-time all-Atlantic Coast Conference performer missed the opener when he was suspended for breaking a team rule. Andrews started in his place and ran for 254 yards in the loss to the Commodores.
Barclay returned with a 60-yard day as Andrews' backup in the 31-3 loss at Nebraska last week, and again was on the sideline behind Andrews against East Carolina. But he didn't need long to make his presence felt, scoring three TDs in the first half to take sole possession of the school's career rushing touchdown record.
After spinning into the end zone for a 6-yard score on Wake Forest's second drive, Barclay scored for the second time with a 19-yard run through the right side for a 24-3 lead.
Late in the half, Barclay scored again, this time cutting to the outside with a hesitation move that sent defender Kasey Ross sprawling to the turf and scoring from 13 yards out for the 31-6 lead.
Pinkney threw for 292 yards and three touchdowns for the Pirates.