Henrik Zetterberg and Mikael Samuelsson also scored, and Dominik Hasek made 16 saves for Detroit (9-4-1), which won its sixth straight.
Ron Hainsey scored for Columbus (4-7-1) and Pascal LeClaire stopped 23 shots before being replaced by Fredrick Norrena after two periods.
Hainsey's power-play goal tied it at 1 at 6:32 of the second period, but the Red Wings answered with three straight.
Zetterberg slapped in a rebound from the left circle at 8:45, Cleary netted his second goal on a short-handed breakaway with 5:56 left in the period, and Samuelsson backhanded a shot in during a goal-mouth scramble with 4:27 remaining in the middle frame.
Cleary opened the scoring with 2:17 left in the first period, tipping in Chris Chelios' shot from the top of the circle along the right wing boards.
Columbus didn't register its first shot until 11:03 elapsed when Rick Nash directed a drive at Hasek from the left circle. Detroit had eight shots by that point.
Notes: Detroit D Mathieu Schneider missed his third straight game due to an injured groin. ... The Red Wings recalled C Valtteri Filppula from Grand Rapids of the AHL and assigned forward Brad Norton to that team. ... Columbus C Sergei Fedorov played 13 seasons for the Red Wings from 1990-2003, posting 400 goals and 954 points. He was booed every time he touched the puck. ... Hockey Hall of Famer Gordie Howe was in attendance.