Wayne Rooney-led United remained atop the East despite falling to 4-3 with two drawn, but their 14 points are under assault with Toronto on 13 with three games in hand and Columbus and Philadelphia on 13 with one match in hand.
City won for only the second time this season against one loss and five drawn.
Mitrita opened the scoring in the 35th minute on a left-footed shot from the heart of the penalty area.
City missed a golden chance in first-half stoppage time after United's Leonardo Jara fouled NYCFC's Anton Tinnerholm in the penalty area.
But Maximiliano Moralez hit the right post and the visitors lead remained only 1-0 at half-time.
Brazilian striker Heber, who joined New York only last month from Croatian club HNK Rijeka, left-footed home a shot from the left side of the box following a corner to give City an insurance goal in the 56th minute.
Elsewhere, the Los Angeles Football Club dominated Seattle Sounders FC at home, clobbering the visitors en route to a 4-1 win at Banc of California Stadium.
Carlos Vela scored twice in the rout. His first came via a toe poke in the 12th minute and the other in the 55th minute. Vela leads the league in scoring with 10 goals.
Eduard Atuesta added one in the 39th minute, sidestepping Roman Torres and punching it home.