New York quarterback Eli Manning was intercepted three times, giving him an NFL-leading 15 for the season. The Giants are winless in their first six games of the year, their longest losing streak to open a season since they dropped their first nine contests in 1976.
New York then climbed within six points when Brandon Jacobs scored on a 1-yard run in the closing seconds of the third period.
The Giants had the ball twice more with a chance to produce a game-winning touchdown, but wound up punting from their own 24 the first time they had it.
New York then took over at its 11 with 5:21 to play and Manning led a march that reached the Chicago 35. Facing second-and-9, Manning threw a deep pass intended for Brandon Myers. Jennings, however, picked it off to end the final New York threat.
The first interception by Jennings was returned 48 yards for a touchdown midway through the first period.
Chicago moved a half game in front of Detroit for the lead in the NFC North. Detroit can regain a share of the top spot Monday night with a victory over Cleveland.
Cutler went 24-of-36 for 262 yards without an interception. Manning was 14-of-26 for 239 yards while Jacobs gained 106 yards on 22 carries.