Gramatica had joined the Cowboys when an inconsistent Mike Vanderjagt was released last Tuesday.
Marion Barber rushed for two touchdowns and Tony Romo was 20-for-34 for 257 yards for Dallas. Gramatica kicked three field goals, Terrell Owens made eight catches for 84 yards, and Jason Witten added three receptions for 73 yards as the Cowboys (8-4) extended their winning streak to four games.
Eli Manning was 24-for-36 passing for 270 yards and two touchdowns for New York. Tiki Barber rushed for 90 yards on 23 carries and added 53 yards on five receptions, and Jay Feely booted two field goals for the Giants (6-6), who fell two games behind Dallas for the NFC East lead.
Both teams scored 10 points in the fourth quarter.
Dallas had a 10-7 halftime lead.