Renfree was 26 of 37 with TDs covering 37 and 31 yards to Conner Vernon, 16 yards to Desmond Scott and 8 yards to Brandon Connette for the Blue Devils (3-1), who outgained the Tigers 500-152 and are off to their best start since 2008.
Connette also had a 4-yard touchdown run for Duke, which had four turnovers -- two in the red zone, a third returned for a touchdown -- but held Memphis (0-4) to less than 100 total yards until late in the third quarter.
Wynton McManus took an interception 4 yards for a score and Tevin Jones added a 2-yard touchdown run for the Tigers, who led 14-7 in the second quarter but couldn't hold on. The Tigers have lost 35 of 40 games since 2009.
After Jones' TD with 9:17 left before the half, Memphis didn't run another play in Duke territory until there were 5½ minutes left in the game.
Duke scored the final 31 points to turn it into a blowout, and Renfree helped the Blue Devils pull away by leading consecutive touchdown drives in the second half.
His strike to Scott over the middle late in the third quarter made it 24-14 and gave the Blue Devils some breathing room. The TD toss to Connette with 10:27 left essentially sealed it, and Vernon's 31-yard catch-and-run turned it into a full-fledged rout.
Duke will open Atlantic Coast Conference play halfway toward the six wins needed for bowl eligibility. The Blue Devils haven't reached the postseason since 1994, and this marks just the second time since then that they have won three of their first four.
The three wins have each come by at least 20 points, and the only loss came against a Stanford team that has since vaulted into the top 10.
They led this one 17-14 at the break despite a poor first half in which they turned it over three times in a span of 10 minutes, 39 seconds, and gave up a 95-yard kickoff return that led directly to another score.
Yet, Duke scored on three consecutive second-quarter possessions and went ahead for good on Renfree's touchdown pass to Vernon with 4:02 before halftime. It came after Ross Martin kicked a 23-yard field goal and Connette started the scoring with his TD run that made it 7-7.
All of the Tigers' points came as direct results of breakdowns by the Blue Devils. In addition to McManus' pick-six, Bobby McCain had a 95-yard kickoff return that set up the touchdown by Jones.