Tom Preissing made it 3-0 with a power-play goal 14:38 into second after Ottawa scored twice on Marc-Andre Fleury in the opening period when the Senators had a 16-4 shots advantage.
The 19-year-old Crosby, who led the NHL with 120 points, scored the game's final goal at 19:11 for his first playoff point. He also had a goal waved off 37 seconds into the third after Dany Heatley put Ottawa up 4-1 with a power-play goal 28 seconds earlier.
Chris Neil and Mike Comrie added third-period goals, and Ray Emery stopped 23 shots for Ottawa, which went 31-7-8 from Dec. 23 to the end of the season.
Jordan Staal and Sergei Gonchar scored for Pittsburgh, which played its first playoff game since 2001.
NASHVILLE - Patrick Rissmiller scored at 11:46 of the second overtime, and San Jose beat Nashville after blowing a two-goal lead in the opening game of the Western Conference first-round series.
Rissmiller, who scored only seven goals in the regular season, beat Tomas Vokoun with a shot from the edge of the left circle after taking a crisp pass from Patrick Marleau.
San Jose squandered a 4-2 lead after two periods, an advantage built with three goals in the middle frame after the Sharks lost top goal scorer Jonathan Cheechoo to an injured right knee.