Prescott was 18 of 27, shaking off two fumbles and an interception, to lead the Cowboys (5-1) to their fifth straight win.
He showed poise in the fourth quarter while marching the Cowboys on a seven-play, 75-yard drive that ended with a 4-yard touchdown pass to Cole Beasley for an 18-point lead with 10:26 left.
The score left Packers fans stunned at Lambeau Field. They were booing at times following another choppy game for the offense. The four turnovers were a season high for Green Bay (3-2).
Even two-time NFL MVP quarterback Aaron Rodgers wasn't immune from the jeering. Rodgers finished 31 of 42 for a season-high 294 yards.
But the Packers didn't get into the end zone until Rodgers and Cobb connected on a 6-yard touchdown pass with 6:53 left to get within 27-16.
Rodgers accounted for two turnovers with an interception to go with a fumble on first-and-goal at the Cowboys 1 with 1:10 left in the third quarter. The Packers were lined up in an empty backfield at the time.
The Packers had five fumbles on the day, losing three.
It was Green Bay's worst defeat at home with Rodgers as the starting quarterback since a 37-20 loss to the Giants in the 2011 NFC divisional playoffs.
