Trocheck also scored in regulation and Sean Bergenheim scored a goal for the Panthers. Luongo made 37 saves.
"Some nights you see the puck better than others, and tonight was one of those nights," Luongo said.
Trocheck moved the puck back and forth in front of Lehner before slipping it past him in the shootout.
"That's my go-to move," said Trocheck, who scored his third goal of the season since making his NHL debut on March 6. "Luckily there's no video of me doing it in the NHL. I pull that move almost 90 percent of the time."
"We go over every shootout before the game. That was one of his moves he likes to make, and as soon as he brought it to his backhand, I just slid hard knowing he was going to try and put it over my glove," Luongo said.
The Panthers snapped a three-game losing streak. The Senators have lost nine of 10.
"Goaltending was on display tonight," Senators coach Paul MacLean said. "Both goaltenders dictated the game and what the result was going to be."
Three goals were scored in the final four minutes of the second, two by Florida.
Trailing 2-0, the Panthers scored two goals 23 seconds apart. Bergenheim made it 2-1 when his one-timer from the bottom of the right circle hit the post and went in at 17:32.
Trocheck tied the score at 2. He took a pass from Scottie Upshall in front and his wrist shot beat Lehner on the glove side at 17:55.
Aside from that lapse to end the second, Lehner was solid in goal.
"We had a few minutes in the second where we got away from our structure a bit, and they capitalized," Lehner said. "We regrouped in the third and played solid."
The Senators went ahead 2-0 on MacArthur's power-play goal. Patrick Wiercioch fired a shot from above the left circle and MacArthur was able to tip it past Luongo at 16:11 of the second.
Ottawa took a 1-0 lead in the second period on the goal by Stone. Stone took a pass from Erik Karlsson low in the left circle. His wrist shot got past Luongo at 11:34.
It was the second goal of the season for Stone, who was recalled from AHL Binghamton for the second time this season on March 23.
Luongo's play even impressed the Senators.
"You could tell he was in a zone tonight," Turris said. "We gave them those quick ones (in the second) to tie it and let them back in it. ... Luongo made some unbelievable saves to keep them in it and took it through overtime."
Bergenheim thought he had a goal in the first period but officials blew the whistle before the puck hit the net.
MacArthur has 10 points (four goals, six assists) during a seven-game streak against the Panthers. ... Senators forward Bobby Ryan missed his second consecutive game with a lower-body injury. ... Panthers forward Jesse Winchester returned after missing eight games with a lower-body injury.