Along the way, the Lions turned the ball over three times in the second half and allowed Chicago to go 69 yards in three plays for the field goal that forced the extra session.
''Football is a game of mistakes. It's not always going to be perfect,'' Detroit safety Glover Quin said.
The Lions didn't need to be perfect to beat the Bears on Sunday, and the league's last remaining team without a victory finally got one, 37-34. Matt Prater won it with a 27-yard field goal with 2:29 left in overtime.
A week after being benched in a loss to Arizona, Stafford threw for 405 yards and four touchdowns for the Lions (1-5). His 57-yard pass to Johnson set up the winning kick on Detroit's third possession of overtime.
Jay Cutler threw for 353 yards and a touchdown, and he rallied the Bears (2-4) after they fell behind 34-31 on Johnson's 6-yard TD catch with 21 seconds left. Cutler completed passes of 25 and 24 yards to Alshon Jeffery, and then a pass interference call set up Robbie Gould's 29-yard field goal that tied it.
''The offense works when we execute,'' Bears running back Matt Forte said. ''Whether it's two-minute or regular offense, if you don't execute it's not going to work.''
Here are a few things we learned from Detroit's victory over the Bears:
MARVELOUS MEGATRON: Johnson is still quite dangerous if he's single covered by a rookie. The Detroit receiver caught six passes for 166 yards, and on the key play in overtime, Stafford rolled out to his right and threw deep to Johnson, who was one-on-one with Bears rookie Harold Jones-Quartey. Johnson won that battle and came down with the ball.
Johnson had help from other receivers as well. Lance Moore had five catches for 106 yards and a touchdown.
RED ZONE PROBLEMS: The Bears gave themselves plenty of chances, but didn't capitalize. Chicago was in the red zone eight times and managed only three touchdowns. On one drive deep into Detroit territory, the Bears came away with no points when Cutler was intercepted in the end zone.
TURNOVERS: The Lions still aren't making things easy on themselves. In the second half, they lost two fumbles and an interception, which led to 18 Chicago points.
The Lions nearly had another turnover at the end of the first half, but Golden Tate crossed the goal line and was ruled to have secured possession of Stafford's pass before the ball was pried free - so that play was changed from an interception to a Detroit touchdown.
BOUNCEBACK: Stafford took a step forward after he was benched a week earlier. He hadn't even surpassed 300 yards passing in a game this season before Sunday.
''Last week was last week. I don't think you look at anything based upon that,'' coach Jim Caldwell said. ''Those things get behind us rather quickly.''
NEW VANTAGE POINT: Offensive coordinator Joe Lombardi has taken a lot of heat for Detroit's sputtering offense. He coached Sunday's game from the booth high above the field, the first time this season he'd done that.
''Joe had really wanted to go up there previously and it just happened that it made sense this particular time and just to change his vantage point,'' Caldwell said. ''It's not like it's a monumental feat. That wasn't the key to it. The key was what happened on that field. Our guys played well.''
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