Thompson, who also grabbed six rebounds, was a nearly perfect 6-of-7 from the field and sank both free throw tries in the Buckeyes' (15-4, 5-2 Big Ten) fourth win in their last five outings.
Deshaun Thomas and Lenzelle Smith both scored 11 for Ohio State. The Buckeyes outrebounded Penn State (8-12, 0-8) 38-25.
Jermaine Marshall led the Nittany Lions with 16 points and D.J. Newbill added 15.
Penn State shot just 29.2 percent in the first half and failed to make a shot during an 11-minute stretch.