Mannino, making just his second appearance, was impressive as Chicago dominated and outshot the Islanders 42-19. He stopped Martin Havlat, Ben Eager and Patrick Kane on partial breakaways.
Kane and Kris Versteeg scored for Chicago, which lost its second straight game and fourth in five.
Blackhawks goalie Nikolai Khabibulin made 15 saves as he returned to the net for the first time since Feb. 11, when he aggravated a groin injury in Atlanta.
Mannino made his NHL debut in November, playing 13 minutes in relief of Joey MacDonald, in a 7-2 loss at Boston.
On Sunday, MacDonald missed his third straight game with a knee injury he sustained Tuesday in Toronto. Mannino was backed up by Yann Danis.
New York improved to 2-1-1 on a season-high six-game road trip.
Chicago outshot New York 12-6 in a scoreless first but neither team was able to sustain pressure.
Mannino was especially sharp early in the second as the Blackhawks controlled play. He stopped Havlat and Eager on partial breakaways, Duncan Keith on a 2-on-1 and Versteeg from traffic in the slot.
Streit's power-play goal with 7:41 left in the second made it 1-0. He fired a high screen shot from the top of the left circle past Khabibulin's stick side.
Less than a minute later, Mannino stopped Kane on a partial breakaway.
Versteeg tied it at 1 with 4:20 left in the period. After Havlat's backhander hit the post, Versteeg pushed in the loose puck.
Park and Nielsen scored 1:20 apart to give New York a 3-1 lead.
Park beat Khabibulin between the legs from the left circle with 2:11 left, and Nielsen swept in a rebound of his own deflection for a power-play goal with 51 seconds left in the period.
Streit extended it to 4-1 with his second power-play goal at 7:46 of the third. He beat Khabibulin with a high drive from the blue line.
Kane scored on the power play with 1:43 left on a rebound to complete the scoring.
Notes: At Bridgeport of the AHL, Mannino was 13-11-2 with a 2.96 GAA in 27 games. ... Chicago RW Patrick Sharp has resumed skating. Sharp, who has 23 goals in 54 games, has missed the last 13 with a left knee injury.
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