Crosby's kick completed the Packers' comeback from a 21-7 halftime deficit.
On third-and-10 from his 21, Rodgers took advantage of yet another free play after defensive end Michael Johnson was whistled for offside. Officials let the play continue and the two-time NFL MVP found Allison on about a 40-yard pass before the receiver beat a couple defenders for more yards.
Crosby took care of the rest for the Packers (2-1).
The winless Bengals (0-3) won the toss in overtime but went three-and-out on their opening drive. It was so loud at Lambeau Field that they had to call timeout before their first overtime snap.
