Virginia guards Joe Harris, left, and Justin Anderson realize that a win over Duke would go a long way toward the Cavaliers’ at-large hopes. (Patrick Semansky/AP)

No more than 30 seconds had passed since the final buzzer sounded on Virginia’s win over Georgia Tech on Sunday when Athletic Director Craig Littlepage grabbed the in-house microphone at John Paul Jones Arena and immediately turned the focus to the biggest game of the year.

“We need each and every one of you Thursday night at 9 o’clock,” he said. “Bring your roommates, neighbors, business partners. Bring the person that pumps gas for you. . . . Bring whoever you can. We need it loud. We’re gonna rock them on Thursday night.”

Virginia is in the midst of a 15-game winning streak at home, a feat that hadn’t been accomplished in Charlottesville since Littlepage was a Cavaliers assistant coach and Ralph Sampson was patrolling the lane at old University Hall. But it’s the next contest in Virginia’s new digs that will prove to be the most important going forward.

The Cavaliers take on No. 3 Duke on Thursday in a matchup that could become a deciding factor as to whether Virginia hears its name called for a second year in a row on Selection Sunday. The Cavaliers remain one of the more intriguing, and confusing, bubble teams in college basketball this year, with an NCAA tournament profile that features more losses to Colonial Athletic Association competition (three) than losses to teams ranked in the Ratings Percentage Index top 25 (two).

The Cavaliers (19-8, 9-5) were ranked No. 71 in the RPI as of Wednesday, below fellow ACC bubble team Maryland, despite a road win at Wisconsin and triumphs over the Terrapins, North Carolina, North Carolina State and Tennessee earlier this season. But the efficiency-based rankings at list Virginia as the No. 17 team in the country.

The game against the Blue Devils (24-3, 11-3), meanwhile, represents Virginia’s last chance to score a marquee victory before next month’s ACC tournament. The Cavaliers haven’t beaten a top five foe since besting then-No. 3 Duke in 2002.

“I think another signature win would solidify them, but you can’t lose games you’re not supposed to,” said ESPN analyst Jay Williams, a former Duke guard.

That’s the problem Virginia encountered early in the season, when senior point guard Jontel Evans missed nine of the team’s first 13 games because of October foot surgery. With him out of the lineup or severely limited, the Cavaliers lost to Delaware — their only loss at John Paul Jones Arena this season — and Old Dominion of the CAA, setbacks that will test the NCAA tournament selection committee’s longstanding mantra that it examines “the whole body of work” for prospective at-large teams.

The Monarchs have just three wins this year, and losing to the Blue Hens meant Virginia missed out on a trip to Madison Square Garden as part of the NIT Season Tip-Off. Instead of potentially facing No. 13 Kansas State, No. 23 Pittsburgh or No. 4 Michigan in New York, the Cavaliers played consolation games against North Texas and Lamar, significant factors as to why Virginia’s nonconference schedule is ranked No. 303 in the country.

“You don’t sit there and play those games, and say what does this mean long range,” said Coach Tony Bennett, whose Cavaliers also lost at George Mason to open the season. “You’re just thankful we’re playing better basketball now, and trying to stay as healthy as possible.”

In that regard, Virginia has received encouraging news over the past week. Freshman center Mike Tobey returned to the lineup against Georgia Tech after missing five games with mononucleosis. He should come in handy against Duke’s Mason Plumlee, a candidate for ACC player of the year. Forward Darion Atkins, who did not play in Sunday’s game because of his ongoing battle with shin splints, will also be available for the Cavaliers. Bennett indicated Atkins is only 60 percent healthy right now.

Since the beginning of the season, though, Virginia’s offense has developed into its most efficient weapon. The Cavaliers have scored 70 or more points in five of their past six games, and Coach Mike Krzyzewski described Virginia this week as playing a style “our fans would really love.”

But when Evans thinks about the Blue Devils, he immediately remembers that they remain the only ACC team he has yet to defeat. He was just a junior in high school when Virginia last upset Duke, on Feb. 1, 2007.

The fans, meanwhile, received Littlepage’s message loud and clear. The school announced earlier this week that Thursday’s game would feature the first sellout crowd of the season.

“It’s gonna be dramatic in here. Electric. Crazy. Any adjective you can find, that’s what it’s gonna be,” Evans said this past Sunday, before answering affirmatively when asked if Virginia needed another marquee win to make the NCAA tournament. Duke “would be a great one to have to end the season.”