Florida has won six of its last nine games. Anaheim has lost its last five.
The Panthers also got goals from Eric and Marc Staal as well as Ryan Lomberg. Sergei Bobrovsky had 29 saves.
Mason McTavish, Frank Vatrano and Dmitry Kulikov scored for the Ducks. John Gibson made 51 saves.
“It was pretty cool, pretty good accomplishment but it was nice to win,” said Verhaeghe, who hit the 30-goal mark for the first time in his career with the overtime winner.
“All game, it felt like we were in control and had a ton of chances. We just could not finish them. They got a couple one-off chances; it was nice to win.”
Anaheim has one of the worst records in the league, but played like the team fighting for its playoff lives instead of the Panthers.
Anaheim scored the first two goals and had a 2-0 lead into the second period.
McTavish opened the scoring at 11:46 of the first by scoring off a rebound.
Vatrano converted on the power play against his former teammates moments after the team played a tribute video for him. Florida traded Vatrano to the New York Rangers last season.
“I thought we had a great first. They are a desperate team over there,” Vatrano said. “They had a good second half and I thought the third was pretty even. We were in it all the way. We scored a late one there, then they get one right back. Overall we could clean up a couple areas, but I thought we played overall a pretty solid game.”
Florida rallied in the second. Eric Staal scored 2:12 into the period with his younger brother, Marc, tying the score 2-2 with 2:37 remaining.
The game remained tied throughout the third before Kulikov gave Anaheim the lead back at 12:51.
Florida tied it 3-3 just over a minute later when Lomberg knocked in a long shot from defenseman Gustav Forsling.
“We know where we are at, we know we needed these points and that was a great response by everyone to stay with it and ultimately get two big points,” Eric Staal said.
“We knew this was important and was a big night. I liked the way my line played whole way. I thought we were engaged and we ended up being rewarded.”
Up next for the Ducks: At Tampa Bay on Tuesday at 4 p.m. PST.