Goals by Talles Magno in the ninth minute and Valentin Castellanos in the 56th minute ensured the Boys In Blue finished their five-match homestand with four wins and a draw.
The defeat ended Columbus' three-match unbeaten run with Caleb Porter's side having not scored in five of their last seven matches.
Story of the match
NYCFC came out much the stronger of the two sides and they were rewarded inside the first ten minutes of the game. Santiago Rodriguez played a short pass to Magno, who slipped a low past Eloy Room.
In the 19th minute, some lovely on the edge of the box interplay ended with Keaton Parks having a go, but he saw his shot blocked.
The visitors, who done little of note so far, nearly found an equalizer in the 28th minute when Derrick Etienne Jr. found Miguel Berry at the top of the box, his shot into the lower right corner deflected out.
Six minutes later, Etienne Jr. rounded into the penalty area as an NYCFC defender went to ground, passing to an open James Igbekeme, his shot too high to trouble the goal.
On the stroke of halftime, Magno would square a pass for Castellanos inside the penalty area, his effort straight at Room.
Last year's Golden Boot winner had an opportunity inside the first five minutes of the second half, meeting a Chris Gloster cross with his head, but he couldn't keep his shot down.
Two minutes later, an almost identical scenario occurred, Room making a fingertip save on Castellanos' latest attempt.
In the 56th minute, the Boys In Blue doubled their advantage. A lofted pass from Maxi Moralez found Castellanos, who deftly chipped over an onrushing Room to make it 2-0.
On 65 minutes, the hosts found a third from a set-piece, Thiago Martins nearly heading home, only for the Crew defense to scramble the ball away.
Late on, NYCFC had two dangerous corners as substitute Alfredo Morales hit the crossbar with the first and ten minutes from time, Magno's header was cleared off the line by Darlington Nagbe.
The defending champions saw out the rest of the contest to extend their unbeaten run to six games in all competitions.
Man of the match: Maxi Moralez
His first since returning from injury was a wildly successful one. Playing in an unfamiliar role as the number six, He completed 90% of his passes, picked up an assist on the Castellanos goal and won nearly 73% of his 11 duels in his 80 minutes on the pitch.