Sullinger left the Buckeyes' previous contest Saturday against South Carolina when he was kicked in the foot. But he showed few ill effects from the bone bruise against Lamar, notching his 24th career double-double.
Ohio State (11-1) got 16 points from Deshaun Thomas.
The Cardinals (8-4) were led by Stan Brown, who netted 10 points to go with 10 rebounds.
Devon Lamb chipped in with 10 points and seven rebounds for Lamar.