Detroit became the first team in the NHL to win a playoff series this year, recording a four-game sweep of the Coyotes.
The Red Wings forged a 3-3 tie on a power-play goal from Niklas Kronwall 4:49 into the second period and it remained knotted until Cleary delivered the game-winner.
Todd Bertuzzi added some insurance less than 2 minutes later by scoring on a wraparound attempt and Patrick Eaves delivered his second goal of the game into an empty net with 36 seconds remaining.
Jimmy Howard, who was in goal for all four of the victories in the series, made 21 saves. He improved his post-season record to 16-8.
Ilya Bryzgalov stopped 35-of-40 shots for the Coyotes.
The Red Wings, who are making their 19th playoff appearance in the last 20 years, are seeking the 12th Stanley Cup championship in franchise history. They finished the regular season as the third seed in the Western Conference behind Vancouver and San Jose.