The Tigers (2-0), leading 27-17 at halftime, scored 21 third-quarter points and held the Jaguars to only 15 yards total offense in the second half.
The Jaguars (0-2) scored on the game's opening possession but White combined with Antonio Gibson on a 55-yard touchdown and Keith Brown returned a blocked punt 27 yards as Memphis took a 17-7 first-quarter lead. It was the first time Memphis returned a blocked punt for a TD since 2012.
Another blocked punt led to White's 21-yard scoring throw to Gainwell and a 48-24 lead in the final minute of the third quarter. Gainwell also rushed for two scores, including a 46-yarder.
White finished 17-of-21 passing for 337 yards. Damonte Coxie had six catches for 112 yards. Memphis outgained Southern 575-258.
Clemson's Xavier Thomas likely back for game vs. Boston College
Clemson defensive end Xavier Thomas is expected to return this week from concussion protocol when the No. 4 Tigers play Boston College.
Nick Saban: There's 'no real timeline' for Tua Tagovailoa's return from ankle injury
Alabama quarterback Tua Tagovailoa will participate in only non-weight-bearing activity for several days before beginning traditional rehab and there's "no real timeline for his return," coach Nick Saban said Monday.
College football conference power rankings
Alabama's hold on the top spot in the SEC has ended, with LSU moving to No. 1 in the rankings.
Capital One Fan Vote: Which one-loss, top-10 team is the best?
Auburn, Florida, Georgia and Notre Dame are all still in the playoff hunt despite an early loss. Which team is best among that group?
Former coach Mark Richt doing OK after heart attack
Former coach Mark Richt says he anticipates a quick recovery after having a heart attack on Monday.
Who is Tua Tagovailoa's backup? Meet Mac Jones
Jones will get his first college start this week in place of injured Tua Tagovailoa. Lane Kiffin remembers a QB recruit similar to Georgia's Jake Fromm.