The teams will play the second leg next Tuesday in Guatemala City with the winner advancing on aggregate score.
NYCFC, the defending MLS Cup champion, is among four Major League Soccer teams still alive in the tournament.
Manuel Gamboa scored in the 60th minute for Comunicaciones to make it 1-1.
NYCFC went back in front on Moralez's volley from 12 yards out in the 65th minute. Rodriguez added his goal about six minutes later.
Talles Magno tapped the ball into the open net with Comunicaciones' goalkeeper occupied in the 19th minute, but video review determined he was offside. NYCFC broke through in the 29th minute on Castellanos' header.