The home defence swarmed all over Cutler, who was given little protection from his offensive line as he completed just 11-of-27 passes for 126 yards and a lone touchdown while getting sacked seven times and throwing four interceptions.
By contrast, his counterpart Aaron Rodgers completed 22-of-32 passes for 219 yards with one touchdown and interception, helping the Packers improve to 1-1 following their shock home loss to San Francisco last Sunday.
The Bears (1-1) also suffered an injury blow when running back Matt Forte left the field with a damaged right ankle early in the third quarter.
"It was a good win for us, we're one and one now, but it's one game," Rodgers told reporters. "We (have) got to get better on offence, the defence played incredible."
The writing was on the wall for Cutler from his opening snap, as D.J. Smith cut a swathe through the Chicago line for the first of seven sacks on the night.
The quarterback was clearly agitated throughout at his protection and is now 0-3 as a Bear at Lambeau with the loss also Chicago's fifth on the trot at the hallowed field.
"I care about this, this isn't just a hobby for me, I'm not doing this for my health," Cutler said when defending his on-field berating of his team mates.
"I'm trying to win football games, I'm trying to get first downs. If we're not doing the little things consistently the right way I'm going to say something.
"If they want a quarterback who doesn't care they can get someone else."
After a scoreless first quarter, Green Bay grabbed first points early in the second when Mason Crosby nailed a 48-yard field goal after Packers coach Mike McCarthy kept the drive alive after he successfully challenged the Bears defence for having too many men on the field.
With all the pre-game talk centred on the high-powered offence for both teams it was the Packers special teams who claimed the opening touchdown.
The home side successfully fooled the Bears with a fake field goal attempt, with Tim Masthay flicking the ball to Tom Crabtree who duly romped the 27 yards for the touchdown and a 10-0 lead.
Cutler was intercepted by Tramon Williams with just over a minute remaining in the first half, allowing Crosby to tack on a 35 yard field goal to extend the lead to 13-0.
Chicago claimed their first points with a Robbie Gould 45-yard field goal midway through the third quarter, coming a play after wide receiver Brandon Marshall dropped a pass in the end zone while wide open.
Marshall, the big off-season signing for the Bears, failed to make a catch until midway through the final quarter.
Crosby slotted a 54-yard field goal early in the fourth to move the score to 16-3 before Rodgers hit Donald Driver deep down the middle for a 26-yard score, the play after another Cutler interception, for a 23-3 lead.
Kellen Davis scored a consolation touchdown for the visitors with just over six minutes remaining.
- Aaron Rodgers