That snapped the Bengals' 10-game losing streak in Denver and sent the Broncos (3-7) to their sixth straight loss, their longest skid in 27 years.
Trailing by a field goal with 1:52 left, the Broncos went three-and-out with Brock Osweiler taking a sack and then firing incomplete to Emmanuel Sanders on fourth-and-4 from his own 26.
Broncos GM John Elway's labeling of his team as soft 48 hours earlier did nothing to harden the Broncos, who stubbornly stuck with formations and schemes that aren't working, such as Mike McCoy's three-receiver sets as his base formation.
Denver defensive coordinator Joe Woods stayed with cornerback Bradley Roby 1-on-1 with A.J. Green, who burned him over and over, including on an 18-yard TD catch with 8:56 remaining that made it 20-10.
Roby's pass interference on Green extended Cincinnati's drive after the Broncos had cut their deficit to 20-17 on Demaryius Thomas' 17-yard touchdown grab.
The Broncos finally forced the punt at the 2-minute warning but went nowhere.
The Bengals took a 13-7 lead into the locker room with Dalton's TD throws of 1 yard to Tyler Kroft and 29 yards to Alex Erickson. The first was set up by cornerback Dre Kirkpatrick's 101-yard interception return and fumble recovery just shy of the opposite end zone after fumbling at the Broncos 15-yard line.
Brock Olivo's special teams units that were responsible for a series of blunders that led to 24 points by the Patriots last week, began to make amends when Shaq Barrett blocked Kevin Huber's first punt, setting up Denver at the Bengals 29.
But McCoy's stubbornness on sticking with three-receiver sets as his base formation continued to cost the Broncos.
Denver emptied its backfield on third-and-3 from the Cincinnati 4 following a 7-yard burst by Devontae Booker and Osweiler's pass was picked off by Kirkpatrick.
Randy Bullock missed the extra point after Dalton's TD pass to Kroft , and because his first completion had lost a yard, Dalton had this oddball stat line: zero passing yards but one TD throw.
The Broncos reached the Cincinnati 3 on their next drive and again lined up with an empty backfield. Only this time, running back C.J. Anderson motioned in from the left, took the handoff and sneaked across the goal line for Denver's first rushing touchdown in the first quarter all season.
Brandon McManus' extra point put Denver ahead 7-6, but the Bengals responded with their second touchdown to go up 13-7. McManus nailed a 61-yarder at the end of the first half, but Marvin Lewis had called a timeout and his do-over was blocked by KeiVarae Russell.
McManus pulled Denver to 13-10 with a 45-yarder in the third quarter.
Osweiler fell to 0-3 since supplanting Trevor Siemian, who was leap-frogged by Paxton Lynch for the first time Sunday when Lynch was the backup and Siemian inactive.
