Cruz, who missed most of 2014 with a knee injury and all of last season with a bad calf, broke free in the end zone for a 3-yard TD with 6 minutes remaining, prompting his trademark salsa dance.
New York beat Dallas in an opener for the first time in nine tries.
Elliott was held to a 2.5-yard average (51 yards on 21 carries), although he had his first touchdown, and the only one for Dallas. Prescott was 25 of 45 for 227 yards.
Copyright 2016 by The Associated Press