The Jaguars lost to the Browns 23-17 in the 2009 season finale in a game Cleveland led handily before the Jaguars scored a late touchdown. The Browns rushed for 214 yards that day, and the Jaguars finished 7-9.
When the teams play Sunday, the stakes will be high for the Jaguars.
Coming off a dramatic 31-24 over the Texans, the Jaguars are 5-4 and tied with Tennessee just one game behind the 6-3 Colts in the AFC South.
They can't afford a loss to the Browns because four of their final six games are on the road, including a game at the New York Giants and then road games at all three division rivals, the Titans, Colts and Texans.
They also hope the way the beat Houston will be a springboard.
Houston cornerback Glover Quin batted a Hail Mary pass in the end zone into the arms of Mike Thomas on the final play of regulation.
A surprised Thomas caught the 50-yard pass inside the 1-yard -line and walked into the end zone to give the Jaguars a 31-24 victory over the Texans just when it seemed as if the teams were headed for overtime.
"Wow, it was crazy. I still can't believe it. That is why it's called the Hail Mary," guard Uche Nwaneri said. "Whether, it s destiny, magic or luck, it's a win. That's a fact.
"I've never, ever in my career as a football player seen that play live. I've always seen on ESPN Classics where it works. But I've never been a part of it.
"It may well be the start of a storybook season."
Thomas said, "What a way to end it, huh? I was a little shocked and stunned."
The last time a Jaguars game ended on a Hail Mary pass was in 2002, when Cleveland's Tim Couch threw a 50-yard touchdown pass to Quincy Morgan to beat Jacksonville 21-20.
It was only the fourth time in NFL history that a regular-season game ended on a game-winning TD pass of 50 yards or more with no time remaining. Two of them took place in Jacksonville games.