Tampa Bay fell behind in the quarterfinal series 3-1 but Roloson finished off the comeback in his 40th playoff appearance. It was his second post-season save, the other one coming in 2006.
The Lightning won a playoff series for the first time since capturing the Stanley Cup seven years ago and they set up an Eastern Conference semifinal meeting with Washington.
The game's only goal came from Sean Bergenheim, who put a slap shot past Marc-Andre Fleury 5:41 into the second period. It was Bergenheim's third score of the playoffs.
Tampa Bay won three games in Pittsburgh during the series and began its comeback with an 8-2 blasting of the Penguins Saturday. The Lightning evened the series at home Monday with a 4-2 victory.
Roloson had only a 24-25 regular-season record in his first year with Tampa Bay. He came to the Lightning after spending two years in Calgary, two in Buffalo, three in Minnesota, four in Edmonton and one with the New York Islanders.
Fleury, who was in goal for all 16 of Pittsburgh's wins en route to the Stanley Cup two seasons ago, made 22 saves.
Pittsburgh had a disappointing season come to a close, one that saw the Penguins forced to play much of the campaign without superstar Sidney Crosby. He suffered a concussion on Jan. 5 and never returned.