Jesus Medina scored his team-leading seventh goal of the season in the 40th minute and Ismael Tajouri-Shradi added his sixth of the campaign 13 minutes later.
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Moralez's tally in the 65th minute was his first of the season and Amundsen netted his first career MLS goal in the 79th. Castellanos converted three minutes later for NYCFC (7-5-2, 23 points), who matched a season-high goal total set in a 5-0 win over FC Cincinnati on April 24.
The offensive barrage was a welcome sight for Luis Barraza, who finished with three saves.
Pedro Gallese made nine saves for Orlando City (7-4-4, 25 points), who were without several key cogs en route to falling to 1-3-1 in their last five matches.
Chris Mueller's absence was not related to contract or transfer issues, a spokesman told the Orlando Sentinel. Tesho Akindele (Canada) and Daryl Dike (United States) represented their respective countries in the Gold Cup quarterfinals, while Mauricio Pereyra sat out the contest while serving a one-match suspension for yellow-card accumulation.
NYCFC scored a first-half goal for the second straight match following a brilliant set-up from Castellanos, who bested Orlando City's Antonio Carlos for a loose ball in the open field. Castellanos' spirited play allowed Medina to gain possession and unleash a powerful left-footed strike that sailed under the crossbar.
Tajouri-Shradi doubled the advantage in the 53rd minute after a brilliant individual effort. He created space against Orlando City's Rodrigo Schlegel at the top of the box before unleashing a left-footed shot that caromed off Gallese's hand and into the net.
Moralez's goal from in close effectively put the match out of reach.
NYCFC picks up statement win vs. Orlando
NYCFC earns a huge 5-0 win over Orlando City, courtesy of five different goal scorers.