Dixon, the American Athletic Conference's Sixth Man of the Year, scored the last five Memphis points.
Guard Joe Jackson added 15 points for the Tigers, who reached the round of 32 for the second year in a row.
Dixon was coming off the only back-to-back games when he did not reach double figures in points.
Forward Isaiah Armwood scored a season-high 21 points and forward Kevin Larsen provided 12 of his 16 points in the first half for George Washington (24-9). Armwood and Larsen combined to make 16 of 22 shots from the field. The rest of the team was 9 of 34.
The Colonials continually threatened to rattle Memphis in the second half even though the Tigers made seven of their first 10 shots from the field after halftime.
It was 45-41 with 14 minutes remaining.
Cheek's 3-pointer and forward Patricio Garino's basket made it 64-62 with less than three minutes left. Garino ended up with 10 points.
Dixon's 3-pointer cut some of the tension for Memphis.
Colonials guard Joe McDonald's acrobatic drive for a basket trimmed the margin to 67-66 with 15 seconds left.
Memphis led 31-26 at halftime lead despite shooting 35.5 percent from the field. The Tigers ran into trouble by scoring only three points in the last four minutes.
Earlier, Memphis built a 10-point lead with just less than eight minutes left in the half.
The Tigers received 10 first-half points from their reserves.