The game was deadlocked heading into the third, but the Red Wings scored four times en route to their fourth straight victory. Cleary has had eight goals while putting together a six-game scoring streak.
Cleary's first goal came with 3:30 left in the second period and gave Detroit a 3-2 lead, but Andy McDonald tied it 37 seconds later.
Cleary then began the big third period with the first of four Detroit goals that came in a span of 3:14. Henrik Zetterberg, Brad Stuart and Tomas Holmstrom also scored in the third period, the last two goals coming on the power play.
Jimmy Howard made 33 saves to get the win. All seven Detroit goals came against Jaroslav Halak, who stopped 31 shots.
St. Louis has lost five in a row.
Celebrity Families of 2014 [PHOTOS]