Janne Niskala added a goal and an assist the Lightning, who tied the game when Bochenski scored with 1:19 to play.
Stamkos, the first overall pick in this year's draft, made a successful NHL debut under new Lightning coach Barry Melrose. Though limited to two shots and a minus-1 rating in his 21:41 of ice time, the 18-year-old player from Canada showed flashes of the talent that drew comparisons to Penguins captain Sidney Crosby -- the top draft pick three years ago.
Crosby gave the Penguins a 4-3 lead with a short-handed, unassisted goal with 2:53 left in regulation. Pittsburgh had erased an early 3-1 deficit with two power-play goals by Petr Sykora.
Sergei Gonchar, the Penguins' top defenseman, left the game in the first period after a hit from David Koci. He didn't return, and the Penguins didn't provide information about his injury.
Tampa Bay sat many of its top veterans, most notably new captain Vincent Lecavalier and Martin St. Louis. Eleven players in the Lightning lineup appeared in seven games or less at the NHL level last season.
The Lightning and Penguins will open the regular season against each other in two weeks with a two-game series in Stockholm, Sweden.