McNabb finished 19-of-30 for 191 yards on a windy day that the Eagles controlled the ball for almost 35 minutes. Westbrook was the workhorse, gaining 131 yards on 33 carries and catching six passes for 72 yards.
New York (11-2) can still win the division title Sunday if Pittsburgh beats Dallas later Sunday.
The Eagles (7-5-1) are back in the playoff hunt after winning their second straight.
However, this is going to remembered as the game the Giants came up empty after a week of scrutiny and media hype following the suspension of Burress for the rest of the season and an investigation into the role of middle linebacker Antonio Pierce in the aftermath of the incident in which Burress shot himself in a Manhattan nightclub.
Pierce, who talked to investigators in the office of the Manhattan district attorney Friday, was nowhere to be found on Westbrook's 30-yard run. He also was three steps behind on a crossing pattern on the clinching TD in the fourth quarter.
Burress, who faces illegal weapons charges, also was missed. Domenik Hixon, his replacement, dropped a 50-yard pass right in his hands with New York trailing 3-0 in the first half.
New York scored late in each half. Kevin Dockery returned a blocked field goal 71 yards for a touchdown on the final play of the first half, and Eli Manning (13-of-27 for 123) found Darcy Johnson for a 1-yard TD pass with 15 seconds to go.
The loss opened up the NFC race again. Until Sunday, the Giants were the dominant team.
The Eagles gave everyone hope, beating the Giants at their own game: defense and ball control.
The Giants, who had overcome the retirement of Michael Strahan, a season-ending preseason knee injury to Osi Umenyiora and a suspension and hamstring injuries to Burress earlier this season in going 11-1, did almost nothing right in the first half.
The one play they got right was the blocked field goal at the end of the first half with Philadelphia looking to extend a 10-0 lead.
With David Akers kicking into a swirling stiff wind, defensive end Justin Tuck got a hand on the ball, knocking it toward midfield. Dockery picked the ball up, stumbled forward in breaking a tackle attempt by Eagles guard Todd Herremans, regained his balance and scooted into the end zone for a score that prevented the Giants from being shut out in the first half for the first time since 2004 against Washington.
The officials held a conference in the end zone and let the score stand.
Until then, the first 30 minutes were marked by Giants' mistakes, particularly by the offense, which never got anything going after an ill-advised end around by rookie Mario Manningham lost 12 yards on their opening drive.
Hixon, who had been outstanding in filling in for Burress on three other occasions, dropped the bomb just moments after Akers kicked a 51-yard field goal on the final play of the first quarter.
Rookie safety Kenny Phillips missed a third-down tackle early on a 77-yard drive that Westbrook ended with a 30-yard run on a play that first appeared to be stuffed at the line of scrimmage.
Even the sure-handed Steve Smith dropped a fourth-down pass on play from the Eagles 42.
Even when the Giants scored, there were mistakes. Pierce was called for two penalties that kept the drive moving.