But they were very different wins, with the Penguins coming from behind while the Ducks held on after making a flying start.
In their Eastern Conference First Round series, the Penguins opened with a 4-3 win over the Columbus Blue Jackets at the Consol Energy Center.
Matt Niskanen (one goal, one assist) and Brandon Sutter (one goal) led the way for the Penguins, while goaltender Marc-Andre Fleury also played a key role with 31 saves.
The Blue Jackets went ahead through Jack Johnson, and they were ahead again when Mark Letestu scored after Jussi Jokinen's equaliser.
Derek MacKenzie extended their lead early in the second period before the Penguins' comeback began.
Beau Bennett and Niskanen ensured the scores were level heading into the third and Sutter netted the winner.
The Ducks made a dream start before holding on for a 4-3 victory against the Dallas Stars at the Honda Center.
Kyle Palmieri, Ryan Getzlaf, Mathieu Perreault and Matt Beleskey all scored in the opening 30 minutes of the match before the Ducks held on to take a 1-0 series lead in the Western Conference clash.
Back in the East, an overtime goal from Dale Weise saw the Montreal Canadiens win a thrilling clash against the Tampa Bay Lightning 5-4.
Steven Stamkos struck a brace from five shots for the Lightning, but Weise delivered with the key play in the 19th minute of the first overtime period.