The Packers had a chance to force overtime in the dying stages of the game, but a two-point conversion attempt was unsuccessful as Mike McCarthy's men fell to a third consecutive defeat.
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The visitors were bidding for their first away victory of the season and first in Wisconsin since 1991, but they found themselves behind in the opening quarter when Mason Crosby converted a 44-yard field goal.
Jim Caldwell's side were playing for the first time since their International Series defeat to the Kansas City Chiefs at Wembley, a result that saw president Tom Lewand and general manager Martin Mayhew sacked by the club, but changes off the field did not appear to have solved matters on it as Detroit struggled to come up with anything on offense.
The Packers also struggled with the ball, however, and the first half saw just three more points as Matt Prater kicked a 49-yard field goal to level things up going into the break.
Indeed, the fans inside Lambeau Field booed the home side's struggling offense, and their mood was not improved early in the second quarter as the Lions registered the first touchdown of the contest.
Brandon Pettigrew was the player to collect a one-yard pass from Matthew Stafford, but it was Ameer Abdullah who created the chance having returned the kickoff 104 yards before finally being brought down just a yard short of the endzone.
Prater's extra point was wide left, but the kicker did nudge his side further in front early in the fourth quarter when his 51-yard field goal sailed between the posts.
The Lions continued to frustrate the hosts' offense, who were limited to three points over the opening three quarters for the first time since 2010, but they did finally make it into the endzone with just under six minutes remaining in the match as Richard Rodgers collected a four-yard pass from Aaron Rodgers.
That left the gap at just two points, but the Lions gave themselves a bit of breathing space when, with less than two minutes remaining, Stafford picked out Lance Moore in the endzone for a four-yard score.
Prater missed the extra point effort for the second time in the match to keep the Packers within a touchdown and two-point conversion of the visitors, and they were handed a break early in the all-or-nothing drive when a James Starks fumble was overturned by replay.
Rodgers did manage to engineer the scoring drive, finding Justin Perillo for an 11-yard touchdown, but the attempted two-point conversion to Davante Adams was unsuccessful as the hosts edged closer to a first home defeat of the season.
However, there was another chance to add more late drama as the match reached a remarkable conclusion, with the Packers recovering the onside kick and getting in to field goal range, only for Crosby to fluff his effort from 52 yards and see the kick blocked as Detroit ended a 24-game losing streak at the home of their divisional rivals.
The result means that Green Bay drop to 6-3 having begun the season with six straight victories, while Detroit improve to 2-7 but remain bottom of the NFC North.