Eberle scored twice in the third period to pace the Islander attack as they fired three goals in the final frame to steal the contest.
Eberle finished with two goals and an assist.
Matthew Barzal and Anders Lee had a goal and an assist for New York.
Casey Cizikas also scored for the Islanders.
Ryan Pulock had three assists for New York.
Robin Lehner picked up the win for the Islanders (45-26-7) turning aside 33 shots.
Adam Lowry and Brandon Tanev each had three point nights for the Jets, Lowry scored twice and added an assist while Tanev had a goal and two helpers.
Jacob Trouba had a pair of assists for the Jets.
Connor Hellebuyck stopped 39 shots for Winnipeg, who dropped to 45-28-4 on the season.
The Jets scored 13 seconds into the contest when Brandon Tanev attempted a wraparound and Adam Lowry had the puck go in off of his right skate.
Lowry scored again at 6:11, tipping a Jacob Trouba shot past Islanders goaltender Robin Lehner.
Brandon Tanev had control of the puck and turned hard toward the right side boards before hitting Trouba with a pass which the Jet defenceman one timed toward the net before Lowry got his stick on it.
Matthew Barzal got New York on the board at 10:19 after Mark Scheifele turned the puck over in the netural zone by passing the puck to the side boards.
Jordan Eberle took full advantage by scooping up the disc before hitting a streaking Barzal on his way to the net.
The Islander centre picked the far corner to snap a 19 game scoring drought and score his 18th of the season.
Brandon Tanev restored the two goal lead at 3:46 of the second period when he fired a puck through a screen, beating Lehner high glove side to make it 3-1.
The goal was his 14th of the season.
With New York enjoying a two-man advantage, Anders Lee tipped in a Ryan Pulock blast past Hellebucyk at 6:06 to pull the Islanders to within one.
The goal was his 28th of the season.
With Anders Lee off for slashing Mark Scheifele tipped a Jacob Trouba slap shot past Lehner at 6:46 to make it 4-2 Jets.
Blake Wheeler fed Trouba at the point before the Jet defenceman one timed it at the net before Scheifele redirected it in the slot.
The goal was his 36th of the season.
Jordan Eberle replied just over a minute later when he knocked a puck past Hellebuyck at 7:49 to pull the Islanders to within a goal.
The goal was his 16th of the season.
Casey Cizikas scored with 1:46 left in regulation to tie the contest at 4.
The goal was his 20th of the season.
Both teams are in action Saturday as New York hosts Buffalo and Winnipeg faces Montreal at home.
SHOTS-NEW YORK 44 WINNIPEG 37