Stamkos' 96 goals over the past two seasons led the NHL, but he had only one assist over the first four games of the series. He had three points on Saturday.
The Penguins, who lead the series 3-2, will get a second chance to advance Monday night at Tampa Bay.
Simon Gagne and Pavel Kubina both scored their first two goals of the series, captain Vincent Lecavalier added his second of the series, and Martin St. Louis had two assists for the Lightning, who set a franchise record for goals in a road playoff game and handed the Penguins their worst home playoff loss.
The road teams has won four consecutive games in the series, and Tampa Bay's victory was the 22nd by a visiting team in 36 NHL playoff games this season.
Pittsburgh's Mike Rupp and Chris Conner scored in the third period.
The margin of victory was the largest for any playoff game this season.
CAPITALS 3, RANGERS 1
In Washington, Mike Green, Alex Ovechkin and Alexander Semin scored, and Washington advanced to the second round of the Stanley Cup playoffs with a win over the New York Rangers in Game 5.
The top-seeded Capitals won the series 4-1, the first time they have finished off a team in fewer than seven games since 1998. Washington blew a 3-1 series edge against Montreal in a 1 vs. 8 matchup last year.
This was also the Capitals' first playoff series under Bruce Boudreau that didn't go the distance. He had led Washington through four seven-game series -- winning only one -- since becoming coach in 2007.
BRUINS 2, CANADIENS 1 (2OT)
In Boston, Nathan Horton scored at 9:03 of the second overtime to give Boston a win and a 3-2 lead over Montreal in their first-round playoff series.
Montreal goalie Carey Price stopped Andrew Ference's wrist shot from 30 feet but couldn't control the rebound. Horton then put his second goal of the playoffs into the open right side of the net.
It was Boston's second overtime win in three days, including a 5-4 victory on Thursday night.
It also was the first win by a home team in the series.
The Bruins, who have won three in a row, can end the series in Game 6 Tuesday in Montreal.