Andrew Cogliano scored the tying goal midway through the second period for the Ducks, who had blown a 3-2 series lead and lost a Game 7 on home ice in four consecutive seasons.
After a rally from an early deficit and a strong defensive performance to back John Gibson's 23 saves, the Ducks ended their ignominious streak and moved halfway to the franchise's second Stanley Cup title.
Anaheim will host the Nashville Predators in Game 1 of the conference finals Friday night.