Canouse's goal in the 44th minute held up as the decisive tally as D.C. United prevailed in the debut of new coach Hernan Losada.
Valentin Castellanos scored the lone goal for NYCFC in the 15th minute.
D.C. United goalkeeper Chris Seitz made three saves, two coming in a tight span late in the match.
NYCFC had a 12-11 edge in shots, and both teams placed four on goal.
NYCFC's Sean Johnson made two saves.
D.C. United was staring at a one-goal deficit before scoring twice in a five-minute span late in the first half.
The first tally came courtesy of Hines-Ike, who was making his D.C. United debut. He received the ball from Junior Moreno and sent a straight-away blast from outside the box past Johnson in the 39th minute.
D.C. United moved ahead in the 44th minute as Julian Gressel took a corner kick and spotted Canouse with some operating room. Canouse was ready and delivered the hard right-legged volley through traffic and into the net for a 2-1 lead.
NYCFC had two solid chances to tie it in the 85th minute. Castellanos had a close-range right-footed shot stopped by Seitz and, after the ensuing corner kick, Keaton Parks' header was grabbed by the goalie.
NYCFC didn't get another top-flight opportunity despite its large possession edge. They held the ball 61.9 percent of the time.
NYCFC also had a solid opportunity in the 68th minute but Jesus Medina sent a left-footer high and wide to the right.
The only time NYCFC could find the net was in the 15th minute. Anton Timmerholm threaded a pass toward the net and Castellanos slid and knocked the ball in with his right foot.