The Bengals opened a 16-7 lead early in the third quarter on a 1-yard touchdown run by Trayveon Williams.
Evan McPherson provided the other points for Cincinnati on field goals of 50, 44 and 31 yards.
Jashaun Corbin had scored on 2-yard run on the last series led by Jones (14 of 16 for 116 yards). Webb then rallied New York with three drives. The first ended with a 31-yard field goal by punter-turned-kicker Jamie Gillan followed by the TD passes for Bachman.
With Gano out, Gillan took over the kicking duties and did a good job. Two of his kickoffs in the second half landed in the back of the end zone and were not returned. While the get-off time on his 31-yard field goal was not the fastest, it was down the middle. Safety Julian Love was the holder for the left-footed kicker.
Besides Thibodeaux and Gano, the Giants also saw wide receiver/returner C.J. Board leave with a rib injury and linebacker and sixth-round pick Darrian Beavers sustain an injury to his left knee in the third quarter.
Cincinnati lost guard Lamont Gaillard to a calf injury in the third quarter.
Bengals: Have Super Bowl rematch with the Rams in Cincinnati on Saturday evening.
Giants: Face the Jets on Sunday in the annual preseason game between the franchises that co-own MetLife Stadium.