Matt Forte ran for 133 yards and bounced back from two costly turnovers as the Bears improved to 5-3 on the season.
Cutler threw a go-ahead five-yard touchdown pass to Bennett early in the fourth for the Bears who extended their winning streak to three games.
Cutler completed 18-of-32 passes for 208 yards during the roller-coaster battle. Bennett, who had missed the previous five games with a chest injury, caught five passes for 95 yards.
It was a crushing loss for quarterback Michael Vick and the Eagles, who gave up a fourth-quarter lead for the fourth time this season.
Philadelphia had an opportunity to score in Chicago's territory with under two minutes left in the fourth. After catching a nine-yard pass from Vick, Jeremy Maclin fell and was tackled at the Bears' 30 yard line on fourth-and-10.
In a matchup featuring two of the NFL's best running backs, Forte outplayed the Eagles LeSean McCoy except for the two fumbles. McCoy finished with 71 yards rushing.
The defending NFC East champion Eagles trail the New York Giants (6-2) by three games.
The Bears entered the game as eight-point underdogs despite coming off a bye last week.
Chicago are third in the NFC North behind undefeated Green Bay (8-0) and Detroit (6-2).