Already renowned for their dramatic comebacks this season, the Bears managed 25 points in the fourth quarter alone, including DJ Moore's decisive touchdown with less than two minutes remaining.
Quarterback Williams threw 361 yards for two touchdowns, and two interceptions, handing the Bears their first playoff win since 2011 and sparking ecstatic scenes at Chicago's Soldier Field.
"We understand that it's 60 minutes of football. We understand and know who we are. We understand what this means to the city," said Williams.
The NFC wild-card clash was the bitter rivals' third battle in the past five weeks. But with the stakes higher than ever, the Bears got off to an atrocious start.
Packers quarterback Jordan Love threw three touchdown passes in an utterly dominant first half, finding Christian Watson, Jayden Reed and Romeo Doubs for a 21-3 lead.
The Bears improved markedly in the second half. Early in the fourth quarter, a D'Andre Swift rushing touchdown closed the gap to five points.
After Love hurled his fourth passing touchdown to Matthew Golden, Williams set up a tense finish, finding Olamide Zaccheaus for a late TD.
And a 25-yard toss to DJ Moore secured the lead, with less than two minutes remaining.
It was Chicago's first win in a playoff game since 2011, extending a resurgent season under rookie head coach Ben Johnson.
"You keep going, you keep fighting, and when the clock hits zero, you'll look up and see who wins," said Williams.