Darlington Nagbe gave Columbus the lead just before halftime. NYCFC evened things up as Jesus Medina took advantage of a scattered Crew defense before Lucas Zelarayan won it in the 62nd minute.
The victory sends Columbus into sixth place in the Eastern Conference standings while a second straight defeat, the first time they have lost two games in a row all season, sees the Boys In Blue slip to seventh.
Story of the match
Columbus was under early pressure as goalkeeper Eloy Room made a fine one-handed save from Valentin Castellanos in the fourth minute and Saad Abdul-Salaam gave away a penalty in the ninth minute after a handball. After a check of VAR, the foul was judged to be just outside of the box.
Darlington Nagbe set up the first chance for the Crew and crossed for a streaking Abdul-Salaam, who was coming down the right and he crossed for Miguel Berry, who forced NYCFC goalkeeper Luis Barraza into an excellent stop.
Room then made a series of saves, blocking an initial shot by Gudmundur Thorarinsson and watching the header on the rebound by Castellanos go wide. On the next sequence, he again saved the initial chance, but center backs Jonathan Mensah and Aboubacar Keita combined to slide in and stop the rebound.
Nagbe opened the scoring in the third minute of first-half stoppage time as he came all the way down the right-hand side and chipped Barraza as the 'keeper came off of his line for his first goal of the season.
Two minutes into the second half, the Boys In Blue were even. A scramble in the Columbus box left Room flat-footed and after the Crew defense couldn't clear, Jesus Medina struck just to the goalkeeper's left to make it 1-1.
With the visitors on the front foot, Room made a trio of stops over the next seven minutes on chances by Medina, Maxi Moralez and Thiago following the goal.
Those saves proved to be important as Zelarayan curled home a free-kick over the NYCFC wall in the 62nd minute, his third goal from a free-kick against the Boys In Blue this season.
NYCFC were presented a great chance in the 78th minute after a corner kick was crossed back in by Thiago. Room palmed it away, but only as far as Ismael Tajouri-Shradi, but his effort was dragged wide.
There were no more chances for either side and the Crew were able to celebrate their maiden victory in their new stadium while the Boys In Blue were unable to take advantage of their superiority for most of the game.
Man of the Match: Eloy Room
While Nagbe scored on a wondruous solo effort and Zelarayan did what he does, the Columbus goalkeeper made several incredible saves to keep NYCFC off the board and even the goal he did allow was only due to a scramble in front of him.