Neal and Leon Draisaitl reacted for the Oilers (8-3-1), who have lost 3 of their last four games while dropping to 5-1-0 on house ice.
"They played the way we would like to play," said Oilers defenceman Oscar Klefbom. "They were more powerful, they won a lot of loose pucks. They didn't give up much, and we didn't produce much. Their goaltender played well, and they found a way to score on us.
"We've got to play better. Specifically in the house."
There was no scoring in the very first period. The Panthers put 9 shots on Oilers goalie Mike Smith as Edmonton sent out 7 shots on Bobrovsky.
The Panthers broke the deadlock 31 seconds into the 2nd period as Aleksander Barkov dropped it back to Ekblad, who beat Smith glove side for his first goal of the season.
Florida added to its lead just over a minute later on when a protective miscue caused Boyle awaiting Smith to commit before sending out the puck into the web.
The Panthers continued their assault and scored their third objective on three shots within a period of 2:05 when another turnover led to Acciari's 4th objective of the season.
Smith was replaced in internet by Mikko Koskinen after Acciari's goal.
Florida made it 4-0 just 49 seconds into the third period on a good wraparound by Dadonov, who sent his sixth through Koskinen's legs.
Draisaitl celebrates 24th birthday
Edmonton finally got on the board with a power-play marker three-and-a-half minutes into the third frame as Neal tipped home his 10th goal of the season and seventh with the man benefit.
The Oilers cut the lead in half with simply under seven minutes to play when Draisaitl commemorated his 24th birthday by slamming home a rebound for his ninth of the year.
Florida put the game away on an empty-net goal by Vatrano, and then got another one with 20 seconds left on a rifle of a shot by Hawryluk with Koskinen back in goal.
The Panthers play the 3rd video game of a four-game journey in Vancouver on Monday. The Oilers start a three-game roadway swing, beginning in Detroit on Tuesday.
Allowing 3 objectives on 3 shots in just over two minutes was a dish for disaster for the Edmonton Oilers on Sunday.
Bobrovsky made 24 stops to improve to 4-2-3.
"I thought our people were prepared they had plenty of energy and it was a strong, great effort, all 60 minutes," stated the Panthers goalie. "I would state we were solid when they scored the 2nd goal, we were still playing with each other, we were still supporting each other. We simply played our game."