Despite the loss, the Colts clinched the AFC South later Sunday when Denver beat Tennessee 51-28.
Indianapolis is in the playoffs but has some major concerns. The Colts were drubbed 40-11 in Arizona two games ago and needed Adam Vinatieri's five field goals to beat Tennessee 22-14 last week.
"We've got some things to clean up, but we certainly came down here with the mindset that we wanted to win this football game and certainly win the division that way," coach Chuck Pagano said.
The Bengals are having their best season at home since 1988, when they won all eight regular-season home games and two playoff games on the way to a second Super Bowl appearance and loss to San Francisco.
They're in position to clinch their first AFC North title since 2009 with two home games in the last three weeks.
Dalton was sharp from the outset, completing 6 of 7 for 81 yards on the Bengals' first drive, including a 29-yard touchdown pass to Marvin Jones. The Colts have been outscored 49-9 in the first quarters of their past six games.
The Bengals got a pivotal touchdown on a reversed call with 1:06 left in the first half.
They went for it on fourth down from the Colts 1-yard line. Green-Ellis took the handoff and appeared to get tripped by nose tackle Josh Chapman, who dived into the backfield and swiped at his feet.
"I hit his foot when he came through," said Chapman, who started celebrating his play.
Green-Ellis said he felt someone trip him. He stumbled ahead, avoided a couple of defenders, landed at the 1-yard line and slid into the end zone. He was initially ruled down, but the Bengals were awarded a touchdown after a review.
The review focused only on whether a defender touched Green-Ellis as he fell near the goal line, not whether Chapman had tripped him in the backfield, referee Jeff Triplette said.