"I had a great hole and I followed my big man [Dustin Crouser's] block and good things usually happen when I get in space," Switzer said. "Princeton came out and played hard but our guys responded."
The Patriots, who scored 61 unanswered points, led 35-3 at the half.
"He's a great back," Princeton coach Randy Peek said of Switzer. "We don't have anything like that on the field. What we don't have in talent I thought we made up for in heart. I thought we fought till the end and we didn't give up. Our offensive line was pushing them around at times and we'd get in the red zone and make a mistake."
George Washington got another three touchdowns in the third quarter, including Switzer's 59-yard scamper to start the half.
On the evening, George Washington rolled up 456 yards on the ground and 557 yards of total offense.
Crouser added 76 yards and a touchdown. Quarterback Trevor Bell completed 6 of 8 passes for 101 yards and also had a 19-yard touchdown run.
"I'm really proud of our guys," Switzer said. "We really played well. [Morton] is going to be with us the rest of the season, and we're going to play for him."
Princeton was led by freshman quarterback Palmer, who had 27 carries for 89 yards. He was 3 for 3 passing for 71 yards.
The Tigers were without standout running back Tahj Sho-Johnson for the third straight game with a leg injury. He is expected to return next week.
George Washington is off next Friday, while Princeton hosts Graham, Va.