After Green gave a light shove to the shoulder of Ramsey, he responded with a two-hand shove that sent his opponent to the ground. Eventually both teams came out and a brawl ensued.
Both players were ejected, making the prospect of watching Bengals-Jaguars even more unappealing.
Green is a UGA alum.
Green finished with one catch for 6 yards on two targets.
Josh Lambo, signed last month after the Jaguars cut Jason Myers, made each of his three field goals to back an offense that was productive for most of the game but stalled in the red zone several times.More news: Outgoing Twitter employee deactivates Trump's account
Bortles completed 24 of 38 passes for 259 yards with a touchdown and no turnovers.
Jaydon Mickens iced the victory with a 63-yard punt return touchdown in the fourth quarter. The Jaguars had outgained the Bengals, 217-37 when Lee scored.
Bortles guided the Jaguars to a remarkable effort on third down, converting 12-of-18 situations.
Ramsey has earned a fast reputation not only for being a shutdown corner but also a smack talker in just his second season in the NFL.