Prescott was playing the Giants in the first visit of his former coach, Jason Garrett, now New York’s offensive coordinator.
A week after giving up a franchise-record 307 yards rushing, the Cowboys allowed Devonta Freeman 20 yards on three carries.
The Giants extended the lead to 14-3 when Kyler Fackrell returned an interception by Dak Prescott 46 yards for a touchdown.
Atlanta cornerback Kendall Sheffield suffered a right ankle injury in the second quarter and was listed as questionable to return.
Smith is one injury to Allen away from completing his remarkable comeback to play in an NFL game again.