Memphis (22-3, 12-0) took control with a run late in the first half and led by at least nine throughout the second half en route to its 14th straight win.
Douglas-Roberts scored the final seven points during a 10-0 Memphis run that put the game away midway through the second half. After a 3-pointer by Andre Allen, Douglas-Roberts hit five straight free throws -- earning a pair of trips to the foul line after stealing the ball and getting fouled on consecutive possessions.
His last basket came when Tulsa's Darold Crow was called for goaltending on his shot from the left side that ended the run and put the Tigers up 58-38. That earned the Tigers' leading scorer a trip to the bench, where he toweled off before sitting out the final 6:39.
Tulsa (15-9, 5-6), with the lowest shooting percentage in Conference USA, struggled against Memphis' stingy defense. The Tigers rank fifth in the nation, allowing opponents to shoot only 38 percent.