Acobello, signed by the Oilers as a minor-league free agent in June, notched his first career goal in second period for a 2-1 Edmonton lead, followed 33 seconds later by Taylor Fedun's initial NHL goal.
But the Panthers got two goals from Scottie Upshall in the third period -- the second coming with 58 seconds left in regulation -- to forge a 3-3 tie.
Upshall was whistled for a controversial tripping call 32 seconds into the extra frame, and 1:23 later Arcobello unleashed a one-timer from the left circle off a pass from Ales Hemsky for the decisive score.
Phillip Larsen scored in regulation and Devan Dubnyk made 20 saves for the Oilers.
Marcel Goc provided a goal and an assist and Jacob Markstrom stopped 23 shots for the reeling Panthers, who dropped a sixth straight and ninth in 10 games.