"Keep your shoulders pointed up the field," Lewis said. "When he does that, he's special."
Cincinnati (3-4) badly needed a win to keep pace in the AFC North heading into next week's matchup with the Washington Redskins in London. The Bengals amassed 559 yards against an injury-riddled Browns defense.
"Again, pleased offensively with how our guys are protecting the football, and doing things the right way," Lewis said. "Impressive job today."
Momentum swung on the final play of the first half, when Dalton lofted a 'Hail Mary' pass into the end zone that was tipped three times before Green hauled it in for a 48-yard touchdown to put Cincinnati ahead 21-10.
"Those are plays that shouldn't happen," Browns head coach Hue Jackson said. "But again, a great player made a great play. It's unfortunate. We have to do a better job."
Replays showed that Green essentially tipped the ball to himself despite being immersed in a sea of defenders. The sixth-year veteran said following Sunday's game that he practiced juggling in high school.
"If it's not the play of the year, it's close," Dalton said. "For how he tipped it ... then he goes and gets it with one hand."
With Browns cornerback Joe Haden out with a groin injury, Green took advantage of corners Tramon Williams and Jamar Taylor and finished with eight catches for 169 yards and a pair of one-handed grabs.
"I don't really pay attention to who's out there," Green said. "It's all about just making plays when you get the opportunity."
It was another rough afternoon for Cleveland (0-7), which lost quarterback Cody Kessler to a concussion in the second quarter. Kessler had just completed an 11-yard shovel pass when he was thrown hard to the turf by Bengals defensive end Carlos Dunlap. At the time of his injury, Kessler was 9 of 11 for 82 yards.
Backup Kevin Hogan took over for Kessler and rushed for 107 yards, including a 28-yard touchdown, but was 12 of 24 for 100 yards and two interceptions passing. Hogan's scoring run was the longest by a Browns quarterbackk in franchise history.
"I'm confident in my ability and preparation," Hogan said. "Obviously, I hope Cody makes a speedy recovery. He's our quarterback and we trust him. But I'm going to do everything I can to make sure I'm ready."
The Bengals made it look easy on their first possession in Sunday's game, driving 75 yards in 2:46 as Hill's 40-yard run helped set up Giovani Bernard's 5-yard touchdown to make the score 7-0.
Cincinnati shut out an opponent in the first quarter for the first time this season before Cody Parkey connected on a 28-yard field goal to put Cleveland on the board early in the second quarter.
Jackson unveiled a new wrinkle with Hogan rushing three times for 37 yards, including a 15-yard run, in the first half. Cleveland averaged 6.3 yards on 15 carries in the first half.
Isaiah Crowell scored on a 1-yard run to cap a 70-yard drive and put Cleveland ahead 10-7.
A 44-yard touchdown pass from Dalton to Brandon LaFell just over two minutes later put the Bengals back in front 14-10.
"Andy's finding me more, I'm getting more comfortable," LaFell said. "Things have been going pretty well the past couple weeks."
Bengals kicker Mike Nugent had a rough afternoon, going 1-for-3 on field goal attempts. Nugent was 13-for-13 this season within 50 yards coming into the game.
Following the Hail Mary at the end of the first half, Hogan scored on a 28-yard run to cut the Browns' deficit to four points early in the third quarter. Hill responded with his 74-yard TD to make the score 28-17, and the Bengals never relinquished control.
Jackson was so exasperated that he ripped off his headphones late in Sunday's game.
"I called the team out," Jackson said. "We've got some things to get squared away, but I take responsibility for it all."
NOTES: Hill's 168 rushing yards were the most for a Bengals running back since Cedric Benson rushed for 189 against the Bears in 2009. ... Bengals TE Tyler Eifert, who hadn't played since last season due to an ankle injury suffered in the Pro Bowl, made his debut late in the first quarter. He had one catch for nine yards. ... Browns CB Joe Haden was inactive for Sunday's game with a groin injury. Tramon Williams started in his place. ... On Friday, Cleveland waived DL Gabe White and signed DB Darius Hillary from the practice squad. ... Six different quarterbacks now have taken snaps this season for Cleveland through seven games.