Trailing 4-3 in the closing seconds of regulation, the Red Wings were on a power play when Pavel Datsyk threaded through a pair of defenders and slipped a backhand pass to Zetterberg, who fired the puck into the net for the equalizer with 3 seconds to go.
Datsyuk had two assists and a goal, Lidstrom added two assists and Zetterberg scored twice in the third period for the Red Wings, who capped a 5-0-1 homestand with the victory.
Jimmy Howard turned aside 23-of-27 shots for the victors.
Jarome Iginla scored twice and added an assist for Calgary. Niklas Hagman and Alex Tanguay chipped in goals and Kiprusoff stopped 33 shots for the losers.