Douglas-Roberts, the Tigers' leading scorer, shot 9-of-16 from the field and was one of five players to score in double figures for Memphis.
The Tigers (10-3) built their lead to 22 midway through the second half and coasted to their fourth win in the last five. The Cardinals shot just 31 percent.
Robert Dozier scored 13 points and Kareem Cooper finished with 12 points and nine rebounds for Memphis. Jeremy Hunt also had 12 points and Joey Dorsey added 11.
James Davis, the Cardinals' bulky 7-foot-1 center and leading scorer at 17.2 points a game, led Lamar (5-8) with 20 points. Currye Todd added 13.
The game was a showdown between teacher and pupil. Lamar first-year coach Steve Roccaforte was an assistant on the Memphis staff under John Calipari from 2001-03.