Winger Hossa was the defending Stanley Cup champions' leading scorer in the regular season but had been shutout in this playoff series before his go-ahead wrister at 16:02 in the second period.
"The hard work finally paid off," the Slovakian, who added his second three minutes after the first to put Detroit 4-2 up, told reporters.
"We needed to get momentum, (Johan Franzen) started us off with two quick goals and I tried to follow him. Anaheim has a lot of big bodies, and you're going to get hit it just depends on how you rebound."
The four-goal tally from Franzen and Hossa boosted the Red Wings to 2-2 in the best-of-seven series, preventing them from going two games down to Anaheim, who had eliminated them from postseason play twice in the last six seasons.
After Anaheim's Corey Perry started the game with a goal 42 seconds into the contest, Swede Franzen beat Swiss goaltender Jonas Hiller twice in the first period.
Hiller, who came into the game having faced 108 shots in the previous two games alone, was pulled in the third after making 28 saves and surrendering five goals.
Mikael Samuelsson and Henrik Zetterberg poured on scores in the third period to give the Red Wings a confidence boost as they head back to Detroit for Game Five on Sunday.
Perry had two goals and one assist for Anaheim, who were without defenseman James Wisniewski after he sustained a bruised lung in Tuesday's Game Three.
Scott Niedermayer had a power-play goal for the Ducks at 10:03 in the third to cut the deficit to 5-3.
