Randolph became the first Wake Forest player ever, and the third ACC player ever, to total more than 300 yards passing and 100 yards rushing. He finished 16-of-21 for 344 yards and ran for another 107, including two clutch runs for first downs on the clinching drive in the final quarter.
Both of his yardage totals were career highs.
Randolph joined Charlie Ward of Florida State and Woody Dantzler of Clemson as the only players to ever throw for 300 yards and run for 100 yards in the same game.
Cornelius Birgs also ran for a TD for Wake Forest (1-1), which lost to Clemson 37-30 in double overtime a week ago.
The Deacons played nearly the entire game without leading receiver Jason Anderson. He sprained his ankle on a 32-yard reception on the second play of the game and left for good, leaving Randolph to make most of the big plays on his own.
He did just that.
Sophomore Nate Morton was Randolph's favorite target on Saturday night, making five catches for a career-best 142 yards and a touchdown.
After the Pirates closed to 10-3 early in the third quarter, Randolph tossed a perfect spiral to a streaking Nate Morton for a 63-yard touchdown, then added a 35-yarder to Chris Davis about five minutes later to make it 24-3.
East Carolina rallied after a couple of mistakes by the Deacons. Willie Idlette fumbled while returning a punt, and Richard Koonce recovered to give East Carolina possession at the Deacons' 48.
James Pinkney then threw a 29-yard pass to Damarcus Fox on third-and-9 to move the ball to the 18, then connected with a wide-open Bobby Good in the corner of the end zone on the next play.
On the ensuing drive, Randolph made one of his few mistakes when he overthrew Idlette over the middle, and safety Zach Baker was there for the interception. Two personal fouls after the turnover cost East Carolina field position, but on third-and-4 from the 14, third-string tailback Chris Johnson scampered around the right end and outran the defense to make it 24-17.
Randolph didn't panic. He moved the Deacons 61 yards in nine plays for their final score, capping the drive with a nifty 18-yard run on a draw. Earlier, he had kept the possession going with runs of 13 and 3 yards on third downs. In all, Randolph accounted for 50 of the drive's 61 yards.
Last week, Randolph was only 7-of-21 for 55 yards.
Wake Forest accumulated 584 yards of total offense, including 451 by Randolph. The total for Randolph was the most since Rusty LaRue set the ACC record in 1995. The 584 yard team total was the most by any Deacon team since 1979.
Pinkey bounced back from a terrible start, during which he threw interceptions on his first two passes. He finished 20-of-37 for 233 yards and the one touchdown.