Kodjia got his ninth goal of the campaign on seven minutes when he headed home Marlon Pack's free kick.
Huddersfield were afforded a great chance to even things up shortly after when Nahki Wells was fouled inside the area as he latched on to Joe Lolley's pass.
Flint was left unmarked from a free kick on 29 minutes and the defender made no mistake as he converted from close range to double the visitors' lead.
Joe Bryan's cross almost ended up making it 3-0, but the over-hit delivery ended up striking the crossbar after the restart.
Lolley was unlucky not to extend the advantage for the visitors when he beat two men from around 20 yards out before wrapping a shot against the post.
Bunn made it 2-1 inside the final 10 minutes with a long-range effort to set up a tense final few minutes for the visitors.
However, City held on to take the three points away from the John Smith's Stadium.