Giants defensive tackle Dexter Lawrence left for the X-ray room in the third quarter.
The Giants trailed 20-10 when Lawrence left, and the team has ruled him out with an elbow injury.
Since the Giants drafted him in the first round in 2019, Lawrence has missed only two games with injuries in his career.
He had three tackles before departing Thursday.
Defensive tackle Rakeem Nunez-Roches (stinger) is questionable to return. So, the top three defensive tackles for the Giants are out of the game currently.
The Cowboys extended their lead to 27-10, with Rico Dowdle scoring on a 4-yard run with 4:23 remaining in the third quarter.
Through three quarters, the Cowboys have outgained the Giants 265 to 160.