Stamkos, who notched 45 goals in the regular season, finally dented the net in the post-season with goals in the first and second periods, joining Simon Gagne and Pavel Kubina with two tallies as the Lightning pulled to within 3-2 in their Eastern Conference quarterfinal series.
Stamkos added an assist while Vincent Lecavalier and Dominic Moore each contributed a goal and a helper for Tampa Bay.
Dwayne Roloson had a shutout until the third period and ended with 31 saves in the one-sided victory.
Mike Rupp and Chris Conner scored for Pittsburgh and Marc-Andre Fleury was yanked from net after allowing four goals on 14 shots in 25 minutes. Brent Johnson let in four goals on 11 shots the rest of the way.
The Pens will try to close out the series again Monday in Tampa.