Doing it again would help give Duke the early edge for another trip to the Atlantic Coast Conference championship game.
Receiver Jamison Crowder on Tuesday struggled to explain the Blue Devils' recent dominance in the series, saying the schools have ''kind of formed a little rivalry in a way.''
Duke has won five of the six meetings since Cutcliffe took over the Blue Devils in 2008.
And for a change, there's plenty on the line for both teams.
Virginia (4-2, 2-0) is the only Coastal Division team without a league loss. Duke (5-1, 1-1) can claim the early inside track to a second straight ACC championship game berth with a victory.
''You better be hungry, and I'm certain (the Cavaliers) are hungry,'' Cutcliffe said. ''They're playing well for a reason, and the thing you have to do, the lesson in that, is to manage your own mentality. ... That's where we have to continue to keep our focus.''
They would all be 2-1 in ACC play, but Duke would hold the head-to-head tiebreakers with both UVa and the Yellow Jackets and will have both the Panthers and Hokies remaining on the schedule.
A victory by the Blue Devils also would make them bowl eligible for the third straight year. Last year was the first time Duke had gone to a bowl in consecutive seasons.
''Being a senior, we want that,'' offensive guard Laken Tomlinson said. ''We want to go ahead and get those wins and hopefully get to a great bowl game and win a bowl game finally. ... Every win that we get, we just get hungrier and hungrier for the next one.''
Virginia coach Mike London, who is 1-3 against Duke since his arrival in 2010, praised Cutcliffe for fielding a team that rarely turns the ball over.
The Blue Devils have an ACC-fewest five giveaways, and should provide a test for an improved Cavaliers defense that leads the league with 19 takeaways.
''He has a scheme and a system that he uses that tries to stretch you vertically and cause you - whatever coverage you're in, man or zone coverage - to make decisions,'' London said. ''Most teams want to stay over top of the balls that are thrown. He has a system that will throw underneath, give it to a guy like Crowder who does a phenomenal job of making yards after catch. ... We have to play defense.''
Duke finds itself in the opposite role it filled last week - when the Blue Devils were coming off a week off and preparing for a Georgia Tech team that had dominated them for most of the past decade. Duke won that one 31-25.
Now it's the Cavaliers who are rested and eager to finally gain a measure of payback from Duke.
''You've just got to come out focused and ready,'' Crowder said.
AP Sports Writer Hank Kurz Jr. in Charlottesville, Virginia, contributed to this report.
Follow Joedy McCreary on Twitter at http://twitter.com/joedyap