Dallas quarterback Dak Prescott was intercepted off his very first pass but recovered to throw for 257 yards and three touchdowns to leave the Cowboys 5-3 for the season and top of the NFC East.
New York, in contrast, have now fallen to 2-7 for the campaign following this latest loss.
The Giants started well and Cody Latimer's touchdown plus two Aldrick Rosas field goals helped them build a nine-point lead midway through a second quarter which was briefly delayed by a black cat strolling across the pitch.
However, Dallas hit back with 10 points in quick succession – including a 42-yard touchdown by Blake Jarwin – to earn a 13-12 half-time lead, and they never looked back.
The last time the Cowboys were in East Rutherford was a month ago when they lost to the stadium's other tenants, the New York Jets.
This time there was no upset result as they added further touchdowns through Michael Gallup and Amari Cooper to secure the victory.