The Bengals had a promising drive stall after an offensive pass interference penalty on rookie receiver Ja'Marr Chase. Rookie kicker Evan McPherson followed by missing a 43-yard field goal wide left.
That set up the Jaguars at the Cincinnati 33 to start their second drive.
Jacksonville needed eight plays to reach the end zone and take a 7-0 lead. The Jaguars picked up six first downs and faced only one third down.
Rookie quarterback Trevor Lawrence had a run of 11 and threw a 17-yard pass to Dan Arnold, who just arrived in a trade from Carolina.
James Robinson scored on a 6-yard run.
Robinson has seven carries for 35 yards.