The Bengals scored on their first drive of the game, with Hill running in an eight-yard touchdown before the Chiefs would reply with a field goal from Cairo Santos.
Cincinnati's other running back Giovani Bernard was the next to find the endzone, scoring a 13-yard touchdown just before the end of the first quarter.
Santos scored two field goals after two consecutive Kansas City drives stalled near the redzone and the AFC West side had to settle with three points on each occasion.
Kansas City had a chance to take the lead going into the half but they had to rely on another Santos field goal to bring them to within two points at the break.
Dalton would get his second passing touchdown of the game in the third quarter, finding Brandon Tate for a 55-yard touchdown to extend the Bengals' lead to nine points.
The Santos show continued for the Chiefs in the second half, with the kicker scoring his fifth field goal of the game to make it 21-15 to the Bengals.
Michael Johnson then forced a fumble from Chiefs tight end Travis Kelce and Hill would run in for his second touchdown of the game before also finding the endzone to convert the two-point attempt following the score.
The Chiefs' redzone struggles dragged on after another good drive halted with 10 yards to go and head coach Andy Reid decided not to go for it, so Santos put up yet another three points.
Hill found the endzone for a third time from a yard away late in the fourth quarter to put the Bengals out of sight, and condemn the Chiefs to their third consecutive defeat despite Santos hitting his mark for the seventh time late on.body check tags ::