Geekie gave the Bruins a 1-0 lead at 4:49 of the first period. He took a pass from Jake DeBrusk, who had curled around the net, and tucked a backhand past Bobrovsky's outstretched stick.
Boston outshot Florida 13-4 in the first period.
“I thought we made really good decisions with the puck in the first period, which led to the most O-zone time in a period, which led to quality scoring chances,” Bruins coach Jim Montgomery said. “Tonight was our best game of the series."
Reinhart tied it 1-1 at 6:23 of the second period. Swayman poked the rebound of Aaron Ekblad's point shot right to Reinhart, who scored off the post from the low slot.
“You play a seven-game series for a reason,” Reinhart said. “It’s not always going to go your way. You try to learn from it. There’s some things we can do little bit better. We’re going to recover and we’re going to come back."