The Hoyas (17-10, 8-7 Big East) likely must beat Rutgers in their last game and win twice in the Big East Tournament to get into the NCAAs.
That's no problem for Sweetney, who recorded his Big East-leading 15th double-double of the season. Sweetney will matchup with Rutgers forward Rashod Kent inside in a battle between the two players who lead the Big East in double-doubles.
"Right now we're just playing our hearts out for a bid," Sweetney said. "We're trying to win every game until this regular season is over."
Sweetney, who also leads the Big East in field goal percentage, hit eight of 12 shoots, including his first four.
"He kept us in it early," Esherick said.
Wesley Wilson added 17 points inside as the Hoya frontcourt sent West Virginia to its eighth straight loss.
WVU (8-19, 1-14) has been eliminated from any postseason play after losing 17 of its last 18 games.
"We couldn't handle Sweetney," WVU interim head coach Drew Catlett said. "He is probably the best low post player in the league. He has big hands and is strong, probably an all-conference player."
Catlett has coached WVU in its last four games after Gale Catlett retired. He will coach the season finale at Pittsburgh.
Both teams started slow. Georgetown missed eight of its first 11 shots, and WVU hit just one of 10 to start the game. The teams shot 38.5 and 36.4 percent, respectively, in a sloppy first half.
The Hoyas, who led the league in scoring in 1985-86, hit three early three-pointers in the second half to open the zone and create inside chances for Sweetney and Wilson.
"We play outside in, that's Georgetown ball," Wilson said. "And when Mike and I are in the game together we can dominate underneath. We'll continue to play hard, because we want to impress the selection committee."
It didn't impress anybody early. WVU's 2-3 zone held Georgetown, which leads the Big East in scoring at 82 points per game, to just 36 points in the first half.
A 12-2 run midway through the second half blew the game open. Leading 42-40, the Hoyas pieced together the push off seven fast break points. The momentum sapped the spirit of WVU, which never got closer than eight points afterward.
"We could sense they were losing confidence," Wilson said. "We had something to lose, and we wanted to play harder than them in the second half."
Georgetown hit 20 of 36 (55.6 percent) shots in the second half, most off layups and putbacks inside.
"We were tight early because the game was important," Esherick said. "The second half we hit enough shots that I could relax some. That was key. We are capable of playing that way for the whole game."
Chris Moss, a senior, finished with 22 points and 13 rebounds to lead the Mountaineers on Senior Night. Chaz Briggs came off the bench to score 14 points. Gerald Riley added 16 for Georgetown.
If WVU loses its last game it will again tie a school-record nine-game losing streak tied earlier in the season.
"Look at us, we don't handle situations well," Catlett said. "We can't shoot outside, and we don't play defense or take care of the ball."
Georgetown has beaten WVU six consecutive times. It is the longest streak in the series, which the Hoyas lead 20-17.
WVU center Chris Garnett was suspended before the game for a violation of team rules. Lionel Armstead also did not play because of a suspension.
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