Semyon Varlamov stopped 36 shots and Ryan Pulock also scored for the Islanders, who cut the Lightning series lead to 3-2.
Game 6 is on Thursday night.
Victor Hedman scored for the Lightning, and Andrei Vasilevskiy stopped 22 shots.
The decisive goal came after the Lightning won a faceoff in the Islanders’ zone. The puck was drawn back to defenseman Kevin Shattenkirk, who fanned on a shot at the right point. Islanders captain Anders Lee raced up the wing to chase down a loose puck. Gaining the Lightning zone, he fed a pass across to Eberle, who scored driving up the right wing.