The 17-year-old is being questioned at the 123rd Precinct.
The man was stabbed just after 11 p.m. Monday during the melee inside the house on Koch Boulevard.
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He was rushed to Staten Island University Hospital North and went into surgery in critical but stable condition.
Police said a scuffle erupted after two uninvited teens pushed their way into the party. They confronted the victim in the backyard in a dispute that was possibly over a girl.
He was stabbed multiple times, including in the chest, left shoulder, right thigh.
Following the stabbing, the suspects fled the scene.
More than 100 young adults were in the house when police responded to the stabbing.
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No arrests have been made and police were investigating into Tuesday afternoon.
Crime scene investigators canvassed the yard and surrounding area searching for any evidence left behind by the suspects.
Neighbors said the party was extremely loud, but they had no idea the home had turned into a crime scene.