Couch missed the first two games with torn scar tissue in his right elbow and his replacement Kelly Holcomb played well, prompting questions about who should be the Browns starter.
But Counch, the first overall pick in 1999, was named the starter by Butch Davis earlier in week and more than rewarded his coach's decision.
"I was proud of Tim Couch," Davis said. "There were two battles he had to fight today. One, he had to beat the Tennessee Titans. The bigger thing was not to just beat the Tennessee Titans, but to beat whatever mystique he thought he had to live up to.
"I think he did an excellent job."
Couch finished 36-of-50 for 326 yards with three touchdowns and an interception.
With the Browns trailing, 28-14, Couch led scoring drives of 80 and 43 yards in the final 2:43 of the fourth quarter. He threw a 12-yard touchdown pass to rookie Andre Davis with 2:35 left and found Dennis Northcutt from eight yards with 12 seconds left to tie it.
"This is the way I've been trying to play all four years," Couch said. "I get hit, try to get back up, and just keep throwing the rock. All I try to do is lead this team and play my heart out and I try to inspire guys to play hard around me."
Couch did not stop there. After the Browns won the coin toss in overtime, he led an eight-play, 65-yard drive, moving his club into position with a 35-yard pass to Davis to the Tennessee 22.
Dawson culminated the drive with his winning kick as the Browns (2-1) won their second straigh game following a gut-wrenching loss to Kansas City in the opener.
"I had to be ready and the offense once again moved the ball down the field like they had to. I just did my part," Dawson said.
"I don't think there is a team in the NFL more deserving to win a game like this, with the times we've been snake-bitten the last few years," Davis said. I talked to the team early in the week and we bought up the first game of the year.
"We said we can let that game do one of two things. It can either build some character for the team, teach us a lesson to fight the entire 60 minutes, or we can let it break us. I knew this football team wouldn't want to surrender."
Davis referred to the bizarre loss to Kansas City, in which the Chiefs got a chance at the winning field goal after time expired because linebacker Dwayne Rudd took his helmet off while play was ongoing.
Steve McNair threw two touchdown passes for Titans (1-2), who lost their second straight game.
"The mindset of our football team is not good," Titans Coach Jeff Fisher said. "It's not healthy by no means right now. I don't have any adjectives to describe them and how it's going to be for the next couple of days, but I will assure you we will come back and be ready to play."
"It's a blow," Titans wide receiver Derrick Mason said. "We've got 13 more rounds to go, and we have to toughen up our stomachs and just keep going. We need to just square our chins up when the next bell rings and just keep going."
It looked like the Titans had the game in hand after McNair, who was quiet the entire afternoon, threw a seven-yard touchdown pass to Kevin Dyson with 5:06 remaining for a 28-14 lead.
McNair's touchdown came two plays after Drew Bennett recovered a fumbled punt by Dennis Northcutt at the eight. McNair completed 15 of 23 passes, but only for 107 yards.
Couch went to work after the Titans' score, leading the Browns 80 yards in 11 plays. He kept the drive alive with a 21-yard connection to Kevin Johnson on third and seven deep in his own territory.
Johnson had nine catches for 90 yards. He was one of nine players with a reception for Cleveland.
Couch also kept the drive alive with a 17-yard pass to Quincy Morgan on third and nine to the Tennessee 23. Three plays later, he found Davis across the middle for 12 yards, pulling the Browns within 28-21.
Northcutt, who was involved on special teams the entire day, recovered the ensuing onside kick at the Tennessee 42. He also returned a punt 74 yards for a touchdown in the third quarter before his fumble.
"You have to catch them in the right alignment," Dawson said. "That's why we shifted, we had eight guys over to the one side and if we had two-on-two over on the left, we were going with it. They actually only had one guy over there so I really felt good about it. It worked out great."
Couch got his team into position to send the game in overtime, keeping the drive alive with a 12-yard pass to Davis on third and 11 to the Tennessee 13. He capped the drive by finding Northcutt in the right flat, where he eluded cornerback Mike Eckols before finding his way into the end zone for an eight-yard score.
Couch also started hot, going five for five on the Browns' first possession that he capped with a 14-yard throw to Davis.
Davis finished with five catches for 99 yards.
The Titans answered later in the first quarter on Eddie George's two-yard run. Questionable all week with a foot injury, George managed just 59 yards on 23 carries.
McNair found backup running back John Simon with a 12-yard touchdown pass 6:05 into the second quarter and the Titans took a 21-7 lead with under three minutes left in the half when cornerback Andre Dyson brought back an interception 16 yards for a score.
Northcutt pulled the Browns within a touchdown with his punt return with 1:25 left in the third.
Notable deaths of 2014 [PHOTOS]