Geekie gave the Bruins a 1-0 lead with a power-play goal at 6:02 of the first period by pulling in a loose puck that deflected off Panthers defenseman Niko Mikkola off a point shot from Mason Lohrei.
It was Boston's first power-play goal in eight games.
Evan Rodrigues tied it 1-1 at 15:29 of the first with a power-play goal, flipping a shot over the glove of Swayman from in front of the net off a shot from inside the blueline by defenseman Uvis Balinskis. It was his first goal in 16 games.
"I think that's the best game we have played in quite some time," Rodrigues said. "You want the result, want the two points, but this is not one we hang our heads in or sulk around."
Pastrnak made it 2-1 at 16:11 of the second, scoring off Geekie's pass from the left circle.
Reinhart tied it 2-2 43 seconds into the third period. Aleksander Barkov drove toward the net before sending a cross-ice pass to Reinhart in front of the net.
"I thought we did the right things, played the right way, and had a lot of puck possession in their zone," Barkov said. "It's not the end result we wanted, but we did a lot of good in this game."
Oliver Wahlstrom made it 3-2 at 2:06 of the third, scoring his first goal with the Bruins after pouncing on a loose puck from a Charlie McAvoy shot attempt near the front of the net and sweeping it underneath Bobrovsky.
Wahlstrom, a lifelong Bruins fan from Portland, Maine, who also attended Boston College, scored his first goal with the Bruins. He was claimed off waivers from the New York Islanders on Dec. 14.
"It's pretty cool, I grew up watching this team since I was little, going to TD Garden with my dad," Wahlstrom said. "I want a lot more (goals), so, I have to get to those areas [around the net] and get my shot off, just keep going. This is big. The guys have had belief in this room since I have been here. There was no real panic."
The Bruins had been outscored 24-11 during their losing streak.
"Obviously, [the Panthers] were pushing hard and are a very good offensive team," Sacco said. "They found a way to tie it, but we showed some resiliency in overtime and found a way to get one, right near the end as well. We had to keep playing. We put ourselves in that situation and had the opportunity to grab that extra point in overtime."
NOTES: McAvoy's assist gave him 20 points in a season for the eighth time in his career. The only other Bruins defenseman with at least 30 points in each of their first eight seasons with the team are Ray Bourque (21 seasons), Bobby Orr (nine) and Brad Park (eight).