Girardi's decisive tally first went off Brian Gionta's skate before it was directed past Bruins goalie Tuukka Rask off a feed from Alex Killorn from the right circle. Rask (24 saves) dropped to 10-9 lifetime in overtime playoff games.
Nikita Kucherov (6th playoff goal), Steven Stamkos (3) and Brayden Point (3) also scored for the Lightning, who have won three straight after a 4-1 victory in Game 3 Wednesday and a 4-2 victory in Game 2.
Patrice Bergeron (6) had two goals and David Pastrnak (6) added another for Boston, which has been outscored 12-6 since a 6-2 win in the series opener.
Game 5 is Sunday in Tampa, Fla.
Boston lost defenseman Torey Krug to an apparent left leg injury after his ankle appeared to buckle against the boards on a hit late in the third period. Krug skated off the ice gingerly before being helped down the tunnel.
Tampa Bay scored twice in the first 10 minutes of the game.
Point split two defenders and put in his own rebound off Rask's pads less than five minutes in.
Kucherov made it 2-0 with his NHL-leading 27th playoff goal since 2015 on a one-timer from the right circle on a Lightning power play at 9:53.
Pastrnak cut the Bruins' deficit to 2-1 with 4:32 left in the opening period, batting in a popped-up rebound that flew right to him in the left circle.
Bergeron converted a well-executed give-and-go with Krug behind the net to beat Andrei Vasilevskiy (29 saves) and tie the game at 2 only 2:04 into the second.
Bergeron's tip-in off a pass from Brad Marchand in the slot gave the Bruins a 3-2 lead with 13:24 left in the third, but Stamkos had the game tied again after powering his one-timer past Rask with 7:04 remaining.
Marchand, who has made headlines during the playoffs for licking the Toronto Maple Leafs' Leo Komarov, went to do the same to Tampa Bay's Ryan Callahan in the second period. Callahan responded by shoving Marchand in the face.
Boston made tweaks before Game 4 by inserting forwards Ryan Donato and Gionta into the lineup on the third line in place of forwards Riley Nash and Danton Heinen. David Backes was relegated to the fourth line.
--Field Level Media
Tampa Bay | Boston | |
Steven Stamkos 2 | Points | Patrice Bergeron 2 |
Steven Stamkos 1 | Goals | Patrice Bergeron 2 |
Steven Stamkos 1 | Assists | Torey Krug 2 |
Nikita Kucherov 1 | Power Play Goals | Patrice Bergeron 1 |
N/A | Short Handed Goals | Patrice Bergeron 1 |
Andrei Vasilevskiy .906 | Save Percentage | Tuukka Rask .857 |
Andrei Vasilevskiy 29 | Saves | Tuukka Rask 24 |
Team | Shots | Goals | Power Play | Penalty Kill | Penalty Mins | Face Offs Won |
Tampa Bay | 28 | 4 | 1-4 | 2-4 | 8 | 22 |
Boston | 32 | 3 | 2-4 | 3-4 | 8 | 36 |