"It was a battle. They played hard all night," Bergeron said. "It was a tough game, we found a way."
Tomas Vokoun made 38 saves for the Penguins one game after he was yanked from the net after giving up three quick goals in the first period.
David Krejci also scored for Boston in the first period. He leads the playoffs in scoring with nine goals and 12 assists.
Chris Kunitz scored Pittsburgh's only goal in the second.
That left it 1-1 after two periods, and it stayed that way through two more. But 4:41 before the second overtime would expire, Brad Marchand grabbed the puck along the left-wing boards and centered it, where Bergeron redirected it past Vokoun and into the net.
"That was a great play by March," Bergeron said. "I think the speed of March and, I guess, our chemistry. I just was trying to get open going to the net, and he found my stick."
That set off a celebration in Boston the first for the Bruins at home this series after they won the first two games of the series in Pittsburgh 3-0 and 6-1. It is the first time all season that Pittsburgh has lost three consecutive games.
The good news for the Penguins: The last of three teams to blow a 3-0 lead in an NHL playoff series was Boston, which lost four in a row to Philadelphia in the 2010 Eastern Conference semifinals.
After two Boston blowouts, the Penguins matched the Bruins and even outshot them 39-25 in regulation including a third period in which Pittsburgh held a 14-4 advantage despite two Boston power plays.
• Boston 2, Pittsburgh 1 (OT)
Bruins lead series 3-0
• Chicago at Los Angeles, 7 p.m., NBCSN
Blackhawks lead series 2-1