The Crew – subject of relocation talk – stunned high-flying Atlanta United in a penalty shoot-out last week to stay alive in the post-season, against all odds, and Columbus drew first blood at home to New York City on Tuesday.
Ola Kamara, Artur, Justin Meram and Harrison Afful were on target for the Crew as New York played almost 40 minutes with 10 men following a red card to Alexander Callens.
New York captain and Spain's all-time leading goalscorer David Villa pulled a goal back 12 minutes from time to keep his team's hopes alive.
Crew fans turned out in force at Mapfre Stadium as the club's owners consider a move to Austin, Texas.
And they had plenty to cheer about after Kamara opened the scoring in the sixth minute, the Crew forward bundling the ball home from close range.
New York were dealt a blow seven minutes into the second half when defender Callens saw red following a video review and Columbus made the most of their numerical advantage – Artur doubling the home side's lead six minutes later.
Sean Johnson was unable to keep out Meram in the 69th minute as the Crew raced clear before Villa pounced with 12 minutes remaining to score New York's first play-off goal since their inception in 2015.
Villa's strike offered Patrick Vieira's men some hope until Afful waltzed through New York's defence in stoppage time to restore Columbus' three-goal lead.