Cleary scored his first two goals of the season, including a key short-handed effort, to lift the Detroit Red Wings to a 4-1 win over the Columbus Blue Jackets on Saturday night.
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.
The Red Wings outshot the Blue Jackets 37-17.
"We controlled most of the game and we were rewarded," Detroit coach Mike Babcock said.
Hainsey's power-play goal tied it 1-1 at 6:32 of the second period, but the Red Wings answered with three straight.
"We got back in the game early in the second and got it tied 1-1," Columbus coach Gerard Gallant said. "But we got the next goal scored shortly after that."
Zetterberg slapped in a rebound from the left circle at 8:45, and Cleary netted his second goal on a short-handed breakaway with 5:56 left in the period.
Cleary beat everyone to a loose puck in the Blue Jackets' zone.
"I read the bounce and got a good jump on them and went in and tried to be patient," said Cleary, who had only three goals in 77 games last season. "We practise breakaways a lot. I tried to out wait him."
Samuelsson backhanded a shot in during a goal-mouth scramble with 4:27 remaining in the middle frame to cap the scoring.
Columbus, which beat Calgary at home in a shootout Friday night, couldn't put together back-to-back good efforts.
"As soon as they scored the second goal, it was over," Gallant said. "The guys stopped competing and I don't know why."
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.
"I don't know, we got away from our game plan," Leclaire said. "We're a good team when we play simple and we keep everything on the sides. We tried to do a little too much and we got caught flat-footed."
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. ... Hall of Famer Gordie Howe was in attendance.