Englishman Wright-Phillips - the league's top scorer - took his tally to 24 goals with a treble against the high-flying Sounders at Red Bull Arena on Saturday.
A volley in the opening minute, followed by two strikes just after half-time from Wright-Phillips had the Red Bulls in cruise control.
And although Sounders captain Clint Dempsey came off the bench to reduce the deficit with 28 minutes remaining, substitute Tim Cahill quickly restored New York's three-goal cushion.
New York's fourth league game without defeat saw them consolidate fourth spot in the Eastern Conference with 41 points after 29 games.
Seattle, who were crowned US Open Cup champions midweek, had their four-game winning streak ended as they dropped to second on goal difference in the Western Conference following the Los Angeles Galaxy's 2-1 win over Dallas.
Wright-Phillips then poked Roy Miller's cross beyond Sounders goalkeeper Stefan Frei, meaning that Dempsey's goal – almost immediately cancelled out by Cahill – was merely a consolation.
Seattle's loss opened the door for the Los Angeles Galaxy, who came from behind to beat Dallas 2-1 and go top in the West.
Goals from Quincy Amarikwa and Jeff Larentowicz saw second-bottom Chicago leading 2-0 after 32 minutes but United levelled proceedings courtesy of Luis Silva's brace.
Other results saw Columbus Crew beat third-placed New England 1-0 thanks to Federico Higuain's goal, while Portland Timbers and Montreal Impact recorded 3-0 and 2-0 wins over the Vancouver Whitecaps and San Jose Earthquakes respectively.
