Hossa opened the scoring 11:42 in, tapping a loose puck past Montoya for his 400th NHL goal.
"I'm very happy about it, especially because it came in a win," Hossa said. "Since the beginning of the game, we had great chances."
The Blackhawks took a 2-0 lead when Sharp ripped a shot past Montoya at 2:23 of the second period.
The Islanders weren't playing well, but they caught a break with 1:39 left in the period when Hamonic's slap shot from the right point got past Emery. Staios tied it at 10:52 of the third when his slap shot from the left point eluded Emery.
New York had other opportunities earlier in the period, but was turned aside on a 5-on-3 power play that lasted for 1:56. Islanders shots either hit Emery or missed the net.
"That five-on-three was huge," Quenneville said. "It was a great kill."
Chicago wound up with two shots in overtime. Montoya made a save on Hossa's shot, but had no chance at the rebound that Sharp put in.
"I thought at times we looked fatigued," Islanders coach Jack Capuano said. "But our team kept fighting back. Yes, we only got one point, but we need all the points we can get."
Emery is 5-1-2 this season as a backup to Corey Crawford. ... The Islanders were missing several injured players but got forward Michael Grabner back in the lineup after he missed one game because of a groin injury. ... New York is 4-0-2 in its last six games. ... The Blackhawks are off until Sunday when they will host San Jose.
Copyright by STATS LLC and The Associated Press
Arena: Nassau Veterans Memorial Coliseum Location: Uniondale, New York
Referees: Ghislain Hebert, Marc Joannette Linesmen: Ryan Galloway, Anthony Sericolo
Attendance: 10,711 (65.7% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Marian Hossa (12)
(Power Play) Assists: Patrick Kane, Patrick Sharp
Patrick Sharp (14)
Assists: Marian Hossa, Niklas Hjalmarsson
Travis Hamonic (1)
Assists: P.A. Parenteau, Matt Moulson
Michael Grabner (8)
Assists: Steve Staios, Frans Nielsen