Lloyd Sam reduced the arrears within 15 minutes of the restart, but Schoenfeld secured his brace on 80 minutes to seal the victory and his side's playoff berth.
Gregg Berhalter's side travelled to New Jersey knowing that a point would be enough to grant them a smooth passage into the knockout stages.
However, there were no signs early on that they turned up for the draw as Crew started the clash well and took the lead on 17 minutes when Schoenfeld guided Finlay's cross past Luis Robles.
It proved a key save as Finlay doubled Columbus's advantage on 34 minutes, latching on to Tony Tchani's through-ball before firing past Robles for his 11th of the season.
The Red Bulls, who had not dropped points at home since July, gave themselves a route back into the game on 58 minutes when Sam beat Clark at his near post.
It would not prove the foundations of a comeback, however, as Schoenfeld grabbed his second of the night with 10 minutes remaining to seal Crew's top-five finish.