Murray, who was pulled from a 4-3, Game 4 loss after giving up four goals in two periods, had to survive a push from the Lightning before the Penguins scored two late goals.
"It's not my job to worry about [coach's] decision," Murray said. "It's my job to be ready if my name is called, and if my name is called, to go out and play my heart out and compete."
Phil Kessel, Kris Letang, Sidney Crosby, Bryan Rust and Nick Bonino scored for Pittsburgh.
Brian Boyle scored twice for the Lightning, who lost Game 6 in a series for the third consecutive time. Tampa Bay also lost Game 6 of the 2015 Eastern Conference Final at home to the New York Rangers before winning Game 7 on the road (2-0).
"We had a great chance tonight and kind of tiptoed around it a little bit," Boyle said. "We were tentative and weren't aggressive. We weren't on top. We weren't skating."