The Red Wings lead the first-round series 3-2.
The lopsided game took an ugly turn with a few minutes left when Calgary backup goaltender Jamie McLennan slashed Johan Franzen in midsection. That decision might lead to a stiff suspension from the NHL, which gave the Islanders' Chris Simon a 25-game suspension for viciously swinging his stick last month.
In the matchup of the Western Conference's first-and eight-seeded teams, the home team has won each game.
The Flames hope the trend continues Sunday night in Game 6.
Cleary, Zetterberg and Chris Chelios scored in the second period and Zetterberg added another goal early in the third to give Detroit a 4-0 lead.
Calgary's Andrei Zyuzin deflected a shot past Dominik Hasek midway through the final period.
Pavel Datsyuk put Detroit ahead 5-1 with 4:18 left to play and about a minute later, Miikka Kiprusoff was replaced by McLennan.
McLennan was on the ice for less than a minute before he was penalized for slashing and removed from the game with a match penalty and game misconduct.
Kiprusoff made 34 saves and Hasek had 23.
Since winning the Stanley Cup in 2002, Detroit has had a pair of first-round exits and one in the second round - against the Flames three years ago.