A point apiece after Rodrigo Muniz and Jeffrey Schlupp each scored in the second half.
Huddersfield are all but relegated from the Championship despite a draw against Birmingham, who remain in the drop zone.
The Bengals entered last season with Super Bowl aspirations, but QB Joe Burrow was limited to just 10 game due to injury as Cincinnati went 9-8 and missed the playoffs for the first time since Burrow's rookie season in 2020.