The second leg is scheduled for April 13 in Harrison, N.J.
Morris' assist produced the opening goal by Albert Rusnak in the 16th minute.
After NYCFC drew level on a Thiago Andrade short-range volley in the 27th minute, Morris blasted a right-footed shot into the top right corner from near the penalty spot to put the Sounders back on top.
Nicolas Lodeiro's penalty in the 68th minute capped the scoring.
Mexican teams have won the CONCACAF Champions League each of the past 16 seasons. No U.S. team has captured the championship since the LA Galaxy prevailed in 2000.