The Saints (2-4) led by only 7-0 early in the third quarter despite controlling play.
The Saints led, 20-7, early in the third period and convincingly blew it to lose by 36-20.
The Saints responded and again led by 4 with 1 minute 40 seconds to go.
Saints led the match 4-0 with all four scored by Reeves.
In that game, the Saints led 17-7 at halftime and 20-10 after the 3rd quarter.
However Saints roared back and led 16-8 lead with 20 minutes to play.
One of those fourth downs was a fourth-and-inches on their own 38-yard line when the Saints were leading just 17-14 in the third quarter.
With 52 seconds left and the Saints leading, 12-10, the Giants got the ball on their 49-yard line.
Halfway through the third quarter the Saints led 20-7.
Ditka's team has lost four of its five games this season, and in each loss, the Saints led entering the fourth quarter.