McCoy took a quick pitch from Michael Vick and broke through the left side of the line, rambling down the sideline for the decisive score for the Eagles (7-3), who won their third straight and took control of the NFC East.
The crucial score came after Vick had lost a fumble in Eagles territory earlier in the quarter and Eli Manning responded by tossing a 5-yard TD pass to Derek Hagan for a Giants lead.
McCoy gained 111 yards on 14 carries and Asante Samuel pounced on a Manning fumble late in the game to ensure the Philadelphia win.
Vick followed up an historic performance against Washington last week by completing 24-of-38 passes for 258 yards and running in a touchdown.
Manning, meanwhile, was picked off three times while going 20-of-33 for 147 yards with two touchdowns for New York (6-4).