La Salle tied the game at 70 when Rasual Butler hit one of two free throws after GW senior Yegor Mescheriakov committed his fifth personal foul.
The Colonials (14-5, 8-1 Atlantic 10) got the ball back with a little more than 35 seconds left on the clock. Rogers held for the final shot and buried it to give GW the victory.
"We took (La Salle's) A-game, we were able to withstand it," GW head coach Tom Penders told WJFK-106.7 immediately after the game.
The Colonials led by five points at 67-62 late in the second half before a pair of free throws by La Salle forward K'Zell Wesson and a basket and a foul shot by Donnie Carr tied the game at 67.
But Rogers hit a basket, was fouled and made a free throw on GW's next possession to give the Colonials a 70-67 lead. Carr trimmed the lead to one with a pair of foul shots. He then forced Rogers into a five-second call by closely guarding him. Butler's foul shot then tied the game.
Rogers scored a game-high 29 points and recorded five steals to lead GW, while Mescheriakov registered a double-double with 14 points and 10 rebounds.
The Colonials led 32-31 near the end of the first half, but La Salle (8-12, 4-6 A-10) went on a 7-0 run, started by a Carr three-pointer, to take a 38-32 lead into halftime.
The Colonials stay on the road and play at Virginia Tech Saturday at 2 p.m.
