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The hosts opened the scoring in the first quarter when Marvin Jones produced a diving catch to collect Dalton's 29-yard pass in the endzone.
The Bengals were forced to wait to extend their lead, but they eventually did so late in the second quarter when BenJarvus Green-Ellis scrambled over from a yard out.
Green-Ellis scored a second from a similar distance early in the third quarter, but this time he powered through the middle of the defense on his way over the white line.
LaVon Brazil showed even more impressive strength midway through the quarter, breaking through five tackles before waltzing into the goal area for a 19-yard score.
The Bengals restored their 14-point lead with 3:12 left in the third quarter when Dalton found Jermaine Gresham wide open in the endzone from a yard out.
They began the fourth quarter in a similar vein as Dalton looped a pass over to AJ Green to open up a 21-point gap for the second time in the match.
Brazil once again led the Colts' revival, getting on the end of a long Luck pass in the endzone to give the visitors hope.
That was quickly extinguished, however, as Dalton looped around before spotting a gap and racing through it for an eight-yard score of his own.
The Colts got the final score of the game when Rogers collected a two-yard pass from Luck, but it was not enough as the Bengals maintained their unbeaten home record this season.