Levens rushed for a franchise-record 190 yards and Brett Favre passed for four touchdowns, including a pair to the tight-end Mark Chmura, in a dominant third quarter.
None of Green Bay's eight previous losses to Dallas were at Lambeau Field, where the Packers extended their franchise-record home winning streak to 22 games. Green Bay was beaten seven times by the Cowboys over the last four years at Texas Stadium, including three play-off games.
The last time the teams met in Lambeau Field was back in 1989, and the Packers rolled to a 31-13 victory. The Cowboys beat Green Bay in Milwaukee, 20-17, in 1991 before the string of games at Dallas.
"Beating Dallas was one of those things we hadn't been able to do since I've been here," said the Packers coach, Mike Holmgren. "Today was our day."
Levens, who also set a career-high with 33 carries and had two touchdowns, broke the single-game club record of 186 yards set by Jim Taylor against the New York Giants in 1961. Levens, who rushed for a total of 701 yards in his first three NFL seasons, has rushed for 1,129 yards as the team's featured back this season.
The win was the sixth in seven games for the Packers, who moved one game ahead of Minnesota and Tampa Bay in the NFC Central. The Vikings were beaten 23-21 at the New York Jets and the Buccaneers lost 13-7 at Chicago.