Jones put the Bengals ahead to stay with his fifth career punt return for a touchdown. Dalton threw three TD passes for the second time in his career, including a short throw that Andrew Hawkins turned into a 50-yard score in the fourth quarter.
Cleveland quarterback Brandon Weeden rebounded from one of the worst debuts in NFL history four interceptions against the Eagles and a 5.1 passer rating by throwing a pair of touchdown passes.
Trent Richardson became the first Browns rookie to run for 100 yards and score on a run and a pass, according to STATS LLC.
Not enough to stop Cleveland from falling to 0-2 for the fifth time in the past seven seasons. Cincinnati improved to 42-36 in the 44-year series, the biggest lead by either team.
The Browns had linebacker Scott Fujita back after his three-game bounty suspension was overturned on appeal. Cleveland missed top cornerback Joe Haden, who served the first week of his four-game suspension for violating the league's policy on performance-enhancing substances. Cornerback Sheldon Brown also was out of the lineup with a shoulder injury.
Dalton took advantage of the depleted secondary by completing 24 of 31 for 318 yards with six sacks and an interception.
The Bengals' defense got shredded during a 44-13 loss in Baltimore on Monday night that matched the most lopsided opening defeat in franchise history. They let Weeden get some confidence and Richardson slip through their fingers, keeping it close.
Weeden completed 26 of 37 for 322 yards with two touchdowns, no interceptions and two sacks for a passer rating of 114.9. Richardson carried 19 times for 109 yards, the first Browns rookie to top 100 yards since Lee Suggs ran for 187 against Cincinnati in 2003.
Phil Dawson's 25-yard field goal with 20 seconds left cut the lead to 34-27, but receiver A.J. Green recovered the onside kick to seal it.
Jones put Cincinnati ahead to stay by slipping away from three Browns and avoiding two others during his fifth career touchdown off a punt return and his first since 2003. He celebrated by jumping and wrapping himself around the padding on the goal post, holding on tightly for several seconds.
Weeden settled down with quick, short throws in the second quarter, when he completed 5 of 7 passes. Richardson, the third overall pick, turned a run up the middle into a 32-yard touchdown for Cleveland's first TD on offense this season.
Dalton made one mistake that kept Cleveland in the game. He sailed a pass that got tipped to linebacker D'Qwell Jackson at midfield late in the third quarter. Weeden threw a short pass to Richardson, who slipped through several tackles on his way to a 23-yard touchdown that cut it to 24-17.
Dalton avoided the rush and threw a short pass that Hawkins turned into the 50-yard touchdown and a 31-17 lead early in the fourth quarter. Weeden responded with a 24-yard touchdown pass to a wide-open Greg Little midway through the quarter.
Cleveland 27, Cincinnati 34
Cleveland 3 7 7 10 27
Cincinnati 7 10 7 10 34
Cin • A.Jones 81 punt return (Nugent kick), 13:13.
Cle • FG Dawson 50, 9:01.
Cin • Green 10 pass from Dalton (Nugent kick), 10:27.
Cle • Richardson 32 run (Dawson kick), 8:05.
Cin • FG Nugent 39, 4:45.
Cin • Tate 44 pass from Dalton (Nugent kick), 11:58.
Cle • Richardson 23 pass from Weeden (Dawson kick), :07.
Cin • Hawkins 50 pass from Dalton (Nugent kick), 10:44.
Cle • Little 24 pass from Weeden (Dawson kick), 7:11.
Cin • FG Nugent 37, 2:09.
Cle • FG Dawson 25, :20.
Attendance • 63,036.
First downs 21 21
Total Net Yards 439 375
Rushes-yards 23-130 25-80
Passing 309 295
Punt Returns 1-9 3-90
Kickoff Returns 6-165 4-103
Interceptions Ret. 1-4 0-0
Comp-Att-Int 26-37-0 24-31-1
Sacked-Yards Lost 2-13 6-23
Punts 4-46.5 3-42.0
Fumbles-Lost 1-1 0-0
Penalties-yards 10-103 6-54
Time of Possession 27:07 32:53
Rushing • Cleveland, Richardson 19-109, Benjamin 2-15, Weeden 2-6. Cincinnati, Green-Ellis 21-75, Dalton 3-4, Peerman 1-1.
Passing • Cleveland, Weeden 26-37-0-322. Cincinnati, Dalton 24-31-1-318.
Receiving • Cleveland, Ogbonnaya 6-73, Massaquoi 5-90, Little 5-57, Richardson 4-36, Smith 3-30, Watson 1-27, Gordon 1-5, Cribbs 1-4. Cincinnati, Green 7-58, Binns 5-66, Gresham 4-37, Tate 3-71, Green-Ellis 3-30, Hawkins 2-56.
Missed Field Goals • None.