The Packers were trailing by 23 points at halftime but outscored the Cowboys 34-10 the rest of way, including two touchdowns in the final 4 1/2 minutes to snatch an improbable victory.
They were aided by two late interceptions tossed by Cowboys quarterback Tony Romo -- the first by Sam Shields set up Lacy's decisive score, and second by Tramon Williams effectively ended the game.
Matt Flynn, again subbing for the injured Aaron Rodgers, completed 26-of-39 passes for 299 yards and four touchdowns with an interception as the Packers (7-6-1) stayed alive in the NFC North title hunt.
Lacy finished with 171 total yards on 21 carries and four receptions.
Romo went 29-for-48 for 358 passing yards with two touchdowns for Dallas (7-7), which remained one game behind Philadelphia in the NFC East.
DeMarco Murray racked up 134 rushing yards with a score on 18 carries and added four catches for 19 yards.
Swim Week Miami Beach 2014 [PHOTOS]