The Hoyas (7-2, 3-1 Patriot League) led 6-0 at halftime on field goals of 18 and 37 yards by Brett Weiss.
When the teams returned for the third quarter, snow had blanketed the field, hampering the passing game. Kempf scored on a 27-yard run on Georgetown's first drive, then Logan added a 34-yard scamper with 2:37 left for a 19-0 lead.
The Crusaders (4-4, 2-1) finally scored with 1:32 to play on Ryan Taggart's 9-yard run, capping a six-play, 45-yard drive that lasted only 57 seconds.
After the two-point conversion failed, Holy Cross recovered an onside kick. Two plays later, the Hoyas got the ball back on a fumble, one of four the Crusaders lost.
Georgetown's Andrew Schaetzke had six tackles, two sacks and three tackles for loss.