LaDainian Tomlinson (left) wanted to eliminate all the risks of trying a field goal in overtime.
"Anything can happen with a field goal," Tomlinson said.
The Chargers (8-5), who won their third straight and seventh in nine games, can clinch their second straight AFC West title with a win next week at home against Detroit.
"To come in here and get a win is really, really big for our guys," San Diego coach Norv Turner said. "And then the way we did it, I think the key for our football team today was we fought hard."
Romo threw a 16-yard pass to Witten with 18 seconds left, lifting Dallas to a 28-27 win over deflated Detroit on Sunday.
The quarterback fumbled near midfield on the drive and the bouncing football was recovered by a teammate after going through a linebacker's hands. The tight end lost the football on the previous possession, less than 1 yard from a go-ahead score.
"I was excited to have the ball back after thinking I lost the game for us," said Witten, who set a franchise record with 15 receptions and a career high with 138 yards receiving.
After the Jets kicked a field goal to pull within two at 17-15 with 1:38 to play, they tried an onside kick that Cleveland recovered. Three plays later on a third-and-4, Lewis broke a number of tackle attempts and rumbled into the end zone for a 24-15 lead.
"It was just a good run that kind of finished things off," said Lewis, who had 118 yards on 21 carries. "I was just trying to stay up. They were trying to strip the ball, so they weren't trying to wrap up and tackle."
Cleveland trails only Jacksonville (9-4) among wild-card contenders in the AFC. "We're in the playoffs right now." Lewis said. "We've got three games left and we're trying to win all of them."
Information from The Associated Press was included in this report.