Detroit fell to 0-11.
"Basically, I didn't do my job," said Hanson, a 10-year veteran.
The Bears benefited from Hanson's misses and improved to 9-2 for the first time since 1991.
Afterwards, Bears coach Dick Jauron made no apologies for the latest win in what appears to be a charmed season.
"I feel real good after that win," Jauron said. "We'll keep that lucky label as long it sticks to us. It was definitely a tough game and it came down to the last kick."
Mike McMahon replaced injured starting quarterback Charlie Batch in the third quarter and drove the Lions 49 yards to the Chicago 21. But with 24 seconds left, Hanson missed a 40-yard attempt well wide to the right after new holder Leo Araguz handled a high snap.
"In this league, it's snap, hold and kick. It doesn't matter if you have a new holder or not," said Lions rookie coach Marty Mornhinweg.
Hanson earlier shanked field goal attempts from 45 and 48 yards, marking the first time he missed three in a game since 1994.
"The second one was perfect and I pushed it right and on the other two, the combination was not right," Hanson said. "I've been in the league 10 years and I know how to adapt and I didn't adapt."
Normally one of the NFL's most accurate kickers, Hanson was voted to the Pro Bowl in 1997 and 1999 and is the second leading scorer in franchise history. But he has missed 10 of 24 attempts this season.
The Lions matched their worst mark since they finished the 1942 campaign with an 0-11 record. The 2000 San Diego Chargers were the last team to start a season with 11 losses.
Chicago scored 10 fourth-quarter points for its latest come-from-behind win. Three of them have come at Soldier Field.
Paul Edinger kicked a 26-yard field goal 59 seconds into the fourth quarter and Leon Johnson scored on a one-yard run with 5:34 left to give Chicago its first lead of the day.
Edinger, who cost the Lions a playoff berth last season with a 54-yard field goal with two seconds left in Chicago's 23-20 win at Detroit in the 2000 season finale, was two for three. He came to Hanson's defense.
"It's Jason Hanson, he's a great kicker," Edinger said. "He just wasn't there today. It happens."
The Lions suffered injury to go with the insult of another defeat, losing Batch for four-to-six weeks with a third-degree right shoulder separation. Batch landed on the shoulder after he was sacked by safety Mike Brown late in the third quarter.
Batch completed 18 of 28 passes for 214 yards in three quarters and left with the Lions holding a 10-3 lead. McMahon, who nearly rallied the Lions in the Thanksgiving Day loss to Denver, was four of nine for 42 yards in relief.
Detroit's James Stewart was unable to run against the NFC's No. 1 rush defense, but caught five passes for 97 yards. He was held to 21 yards on 11 carries, including a three-yard touchdown in the first quarter.
Stewart's score capped a 10-play, 95-yard drive which he highlighted with a 56-yard catch.
Meanwhile, Chicago's James Allen rushed for 93 yards on 25 carries.
Edinger kicked a 46-yard field goal in the second quarter and a 26-yarder in the fourth, but also missed from 39 yards in the fourth.
Hanson's 36-yard field goal in the third quarter capped a 12-play, 73-yard drive. The key plays were an 18-yard pass interference penalty against cornerback Walt Harris and a 29-yard pass from Batch to Lamont Warren.
With Anthony Thomas out a second straight week with a hamstring injury, Johnson was used in short yardage and goal-line situations and scored the winning touchdown with 5:34 left, capping a 14-play, 55-yard drive. Johnson kept the drive alive with a six-yard run on fourth and one to the Detroit 30.
The win kept the Bears tied with St. Louis for the best record in the NFC.
"They still don't respect us," said Bears cornerback R.W. McQuarters. "You look at any TV show or anything, people are saying 'Bears got lucky again this week'. How long are they going to keep saying that? We're not playing with rabbits foots in our pockets."