The Jets (7-7) were at the Bears' 37 and driving for the potential tying score when Chrebet caught a second-down pass and ran it down to the 20, where he fumbled trying to vault a handful of defenders.
Williams, starting for the injured R.W. McQuarters, came up with the ball at the 14-yard line.
"I'm not going to tell guys not to jump, not to run the ball this way when there's eight guys trying to take your head off," Jets Coach Herman Edwards said. "If he jumps and he lands on his feet and he scores, then no one says he's trying to do too much. Then he's made a great play."
Former Jet Leon Johnson and rookie Adrian Peterson rushed for scores for the Bears (4-10), who took a 10-0 lead at halftime and did not have a turnover.
"He (Williams) will end up getting an award for his first NFL fumble recovery," said Bears Coach Dick Jauron "We can say the same thing about Adrian, and his first NFL touchdown."
"We just couldn't execute," Edwards said. We could't get anything going, offensively."
Curtis Martin rushed for 127 yards in a losing effort for New York, which fell two games behind first-place Miami in the AFC East.
Chris Chandler was accurate in the Bears' short-passing game, completing 23 of 28 attempts for 177 yards.
"We knew they were a very disciplined zone defense. There were some holes in the zone if you had the time and vision," Chandler said. "We were very disciplined in our routes and protection, which allowed us to be successful all day."
Johnson carried 15 times for 56 yards and Peterson seven for 39, but it was the injury-riddled Chicago defense that carried the day.
Trailing four minutes into the fourth quarter, 17-10, New York drove from its own seven to the Chicago 14, where a pass interference penalty on cornerback Travis Coleman resulted in a first down.
Pennington, who came into the game as the highest-rated passer in the AFC, hit on 17 of 25 attempts for 146 yards and a touchdown.
The Bears answered with a 12-play drive that resulted in a 48-yard field goal by Paul Edinger, who in the second quarter opened the scoring with a 53-yarder.
The Jets' final drive started at their own 24 with 2:38 to play and progressed slowly.
Faced with a fourth and two, Pennington found running back Richie Anderson for 15 yards to the Bears 42, then completed a five-yard pass to Chad Morton before the 23-yard strike to Chrebet that resulted in the receiver's second lost fumble of the season.
"You know, it's the kind of thing where you don't really think out there, you just react, and that was my reaction," Chrebet said. "You try to make a play. I had a good head of steam going and I could see the end zone."
"Well, that play didn't lose the game for us," Pennington said. "There were numerous plays that I could have made to give us some spark."
The Bears notched just their second victory since starting the season 2-0.
Owning a 3-0 lead with 1:36 left in the first half, Chicago scored the game's first touchdown when Peterson capped an 11-play, 67-yard drive with a five-yard run.
Peterson entered the game with 11 yards on three carries this season, but will get playing time down the stretch with starter Anthony Thomas out for the rest of the season with a broken finger.
The Jets came in flat despite knowing they needed to win to have any realistic shot at their second straight postseason. They got on the board 4:05 into the third quarter after Pennington found Chrebet for a five-yard score.
"I really can't explain it, I don't know why weren't up for it," Jets defensive tackle Jason Ferguson said. "I don't know why we couldn't get up for the game, I really don't."
Chicago regained its 10-point advantage 3:36 later when Johnson took it in from the 2 for a 17-7 lead. The drive was kept alive by a roughing-the-passer call against Ferguson on third and seven from the Jets' 40.
"It was a dumb play, I should know better," Ferguson said.