Cleary's goal 8:11 into the third period gave the Red Wings a decisive 4-2 led and Jimmy Howard turned aside 33-of-36 shots as Detroit, which holds the third seed in the Western Conference, closed out the regular season with a 47-25-10 record.
Tomas Holmstrom, Pavel Datsyuk and Drew Miller also found the net for the Red Wings.
The Blackhawks claimed the eighth and final playoff seed in the West despite their loss after the Dallas Stars fell to Minnesota in a game played later Sunday.
Chicago finished with 97 points, two better than Dallas.
Michael Frolik and Brent Seabrook added goals and Corey Crawford made 27 saves for Chicago, which finished the season with a 44-29-9 mark.