Xavier guard Dee Davis, center, tries to dribble between Georgetown’s D'Vauntes Smith-Rivera (4) and Jabril Trawick, left. (Nick Wass/Associated Press)

Rest was hardly an option for the Georgetown men’s basketball team heading into its most recent game Saturday morning. So when Coach John Thompson III said in the aftermath of an emphatic victory over Xavier, “I think we’re all ready for a nap,” the remark was not completely in jest despite generating laughter throughout the room.

The Hoyas, following a game that tipped off at 9:15 on Thursday night, had less than 36 hours to prepare but notched a 74-52 win that kept them in the conversation for an NCAA tournament berth, albeit a long shot with remaining regular-season games against three of the top four teams in the Big East Conference.

“We’re still in a position where we can play our way into the tournament,” Thompson said. “I know we can play our way in. We do what we’re supposed to do, we take care of our own business, we’ll be okay.”

At least Georgetown (16-11, 7-8 Big East) has had extended time to recover before its rugged closing stretch resumes Thursday night against Marquette at Bradley Center, where the Golden Eagles have won 23 of 25 in conference play. The Hoyas lost the first meeting in overtime, 80-72, at Verizon Center on Jan. 20 and are 2-6 on the road this season.

The Hoyas arrived in Milwaukee, where high temperatures have been in the single digits, buoyed by their most lopsided Big East victory that blunted a two-game slide in which drive and focus were lacking in the immediate stages after tip-off.

A tactical decision announced shortly before the start of Saturday’s game contributed substantially to the turnaround. In a move to get his most energetic player involved right away, Thompson inserted Jabril Trawick back into the starting lineup, and the junior guard-forward responded with 13 points, making 2 of 4 three-pointers while adding four rebounds and three assists.

Trawick, who started the first 14 games, had been coming off the bench since breaking his jaw Jan. 8 during a 70-52 loss to Providence at Dunkin’ Donuts Center. The Hoyas went on to lose five in a row, but when Trawick reemerged at full strength, they won four straight to get back into position for an NCAA tournament bid.

Even with an RPI-building win against the Musketeers, who are in third place in the Big East, Georgetown has much left to do to fortify its NCAA tournament résumé, and beating its final three opponents still might not be enough to earn a fifth consecutive berth.

What’s more realistic for the Hoyas (No. 59 RPI) if they win out is a possible bye in the Big East tournament that begins March 12 at Madison Square Garden. The top six seeds qualify for the quarterfinals and avoid having to play potentially four games in as many days.

“At this point we’ve got three games left, but we’re focusing on Marquette,” Trawick said. “We go take care of Marquette, and then we have the same mindset for the game after that. Right now we’re just focusing on going to Milwaukee and getting a win.”

The Golden Eagles (16-11, 8-6) are in fourth place in the Big East with wins in four of their past five games. They beat Georgetown earlier this season by scoring the first seven points in overtime and making all eight of their free throws the rest of the way after Todd Mayo’s three-pointer tied it with six seconds left in regulation.

Georgetown has not won at Bradley Center in nearly six years. Last season the Hoyas lost, 49-48, but had an opportunity to force overtime when Greg Whittington, who no longer is with the team, was fouled while attempting a three-pointer with two seconds to play and Georgetown down three. Whittington made the first two foul shots before missing the third following a timeout.

“We could have won the game,” said Trawick, who was out for the first meeting this season against Marquette. “I could have made a shot to win the game I think, and then Greg shot some free throws. We’ve just got to go in there and execute and play as a team.”