Georgetown fans cheer the Hoyas during Tuesday’s NIT matchup at McDonough Arena. (Jonathan Newton/The Washington Post)

A packed, partisan crowd and the familiar confines of their own practice gym couldn’t help the Georgetown Hoyas find their shooting range in the early going of Tuesday’s National Invitation Tournament opener against West Virginia.

But after an off-target first half at McDonough Arena, sophomore guard D’Vauntes Smith Rivera erupted for 23 second-half points to lead Georgetown to a 77-65 victory over its former Big East foe.

With it, Georgetown (18-14, 8-10) snapped a five-game losing streak to Bob Huggins’s Mountaineers and earned a second-round NIT date with No. 1 seed Florida State, a 58-53 victor over eight-seeded Florida Gulf Coast, the upstart mid-major that bounced the Hoyas from the NCAA tournament last season.

The date of the Georgetown-Florida State game, to be contested in Tallahassee, will be announced Wednesday.

It was just the second game the Hoyas have won in any postseason in the past six years. And the 6-3 Smith-Rivera got them going, finishing with a season-high 32 points while adding a team-high 10 rebounds and hitting all 10 of his free throw attempts.

“These two guys are going to sleep well tonight,” Coach John Thompson III said of Smith-Rivera and back-court mate Markel Starks, who added 14 points and a career-high seven rebounds.

Picked to finish second in the reconstituted Big East, Georgetown struggled instead this season — battling ill-timed scoring slumps and defensive lapses, as well as injury and academic ineligibility in the case of two key starters.

After missing the NCAA tournament for the third time in Thompson’s decade-long tenure on the Hilltop, the Hoyas were awarded a No. 4 seed in the NIT and drawn against fifth-seeded West Virginia.

It was the teams’ first meeting since the 2011-12 season, the Mountaineers’ last before leaving the Big East for the Big 12. And it was the first men’s basketball game played on campus at McDonough since December 2009.

Despite the cheers of a raucous student section, Georgetown played an ugly first half, clanging untold layups and point-blank shots off the rim. But the Hoyas stayed within range, never trailing by more than four, thanks to early trips to the free throw line that compensated for their sub-30 percent shooting.

A seesaw tussle ensued, with the lead changing hands nine times in the first half.

West Virginia junior point guard Juwan Staten, the Big 12’s leading scorer, did everything for the Mountaineers (17-16, 9-9). A quick-thinking, sharp-eyed ball distributor, he was equally adept at creating his own shot if no teammate was open. And he proved a handful for Starks, who drew the tough defensive assignment.

Staten converted a three-point play to give the Mountaineers their biggest lead of the first half, 33-28. But as the buzzer sounded, Aaron Bowen’s putback pared the deficit to one possession, with West Virginia leading 33-30 at the break.

The Hoyas jumped out with a fury to start the second half.

Smith-Rivera muscled inside for a layup to knot the score, then drilled a three-pointer that prompted a West Virginia timeout. Starks followed with a basket to cap a 7-0 run — the biggest scoring burst of the game — and put Georgetown up 41-36 with 16 minutes 5 seconds remaining.

Smith-Rivera’s hot hand continued, and Starks and Jabril Trawick (12 points) joined in to extend the Hoyas’ advantage.

Afterward, Smith-Rivera credited the screens set by teammates Moses Ayegba and Mikael Hopkins and the pinpoint assists from Starks.

“It was just being in the right place at the right time,” he said.

Huggins, whose 740 victories trail only Mike Krzyzewski and Jim Boeheim among active Division I coaches, didn’t hide his disappointment in his players’ lack of intensity, particularly on defense, saying bluntly that they weren’t gifted enough shooters to defend so lackadaisically.

“We had some guys who could have played a lot harder,” Huggins said. “If you don’t treat the game with respect, don’t put time into it, don’t care about it — it’s not going to treat you very good.”