Armstrong hit Dontayvion Wicks on a 20-yard corner route and Jelani Woods with five seconds left in the first half as the Cavaliers (5-2, 3-2 Atlantic Coast Conference) built a 34-0 lead. The touchdown just before halftime came as intermittent rain began to fall more significantly, sending fans to the exits.
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The victory margin was the Cavaliers' largest since they beat VMI 49-0 in 2013, and largest in an ACC game since they beat Miami 48-0 in 2007.
Earlier in the season, after opening with two impressive wins, the Cavaliers defense was maligned after allowing 699 yards in a 59-39 loss to North Carolina and then losing 37-17 at home against No. 16 Wake Forest.
"We're just playing more physical. We're playing with more passion. We're having fun out there," linebacker Nick Jackson said. "We just got back to going out there and having fun and we're celebrating and having fun, just doing our little things."
The Blue Devils (3-4, 0-3) arrived third in the league with an average of 496.8 yards of offense but mounted just one drive in the first half. It ended when Matt Alswanger banged a 25-yard field goal attempt off the left upright. A fourth-and-5 pass from the Cavaliers' 19 was batted down in the third quarter.
Duke had a first-and-goal chance at the Virginia 1 in the closing minutes, but a first down run yielded no gain and backup quarterback Riley Leonard fumbled on the next play with T.C. Harrison recovering to preserve the shutout.
"To hold the shut out, I mean, that was awesome right there," Jackson, who had 11 tackles, said. "It means all the hard work throughout the week paid off."
Blue Devils coach David Cutcliffe, whose team has a bye week ahead, described the outcome as "something of a gut-check" to rebound from.
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"The approach is finding a way to get better, and the approach is again owning it, which starts with me," he said. "Every one of us are tough-minded enough and have enough character to take this on. That's where it all lies."
Armstrong, second nationally with an average of 410 passing yards coming into the game, had 296 by halftime and finished with 364. He also scored on a 7-yard run and saw Keytaon Thompson turn a shovel pass into a 19-yard completion. Thompson ran it on from the 1 on the next play.
Virginia coach Bronco Mendenhall is not one who would ever apologize for winning, but his respect for Duke's Cutcliffe made the finish tough.
"I admire not only how coach Cut does his job, but why he does his job, and there needs to be more of both in college football," Mendenhall said. "And any time someone doesn't have success doing that, especially now, yeah. I had mixed feelings from halftime on. I know there's a professional part, but there's a personal part. And yeah, it hurts me because of my support of him."
Signs that it might be a tough day for the Blue Devils came quickly. They twice dropped interception opportunities in the first half. The first turned into a crazy play as Jeremiah Lewis made a play on the ball, had it go through his hands and up into the air where Billy Kemp ran under it for a 21-yard gain.
The Blue Devils have a bye next weekend, then play at No. 16 Wake Forest.