Rodgers completed 12-of-17 passes for 181 yards, but was picked off twice as the Packers (3-1), whose current 10-game winning streak is the longest in the series in over 50 years, dating back to Detroit's 11-game surge from 1949-54.
"It's never lucky to get a win in this league," Packers coach Mike McCarthy said. "The way we won says a lot about our resiliency. We were able to get some first downs and run out the clock."
Shaun Hill finished 34-of-54 for 331 yards with two TDs and a pair of interceptions for the Lions (0-4), who haven't won outside the Motor City since October 28, 2007 at Chicago. The NFL record is 24 road losses in a row, set by the Lions from 2001-03.
Hill made his third consecutive start at quarterback in place of Matthew Stafford, who continues to make progress in his rehab from a right shoulder injury.
"We played better as an offense, but all that falls by the wayside when you don't get the win," Detroit wide receiver Calvin Johnson said. "We need to cut down on penalties and execute plays."
Detroit gave the ball back by punting with 6:32 left and never got possession again as Green Bay pounded out six first downs on its final drive.
Charles Woodson returned an interception 48 yards for a touchdown for the Packers, who set a team-record with 18 penalties in Monday night's 20-17 loss at Chicago. In their fourth game, Green Bay lost two fumbles, both on kickoff returns by Jordy Nelson.
Jahvid Best, who started the game despite injuring the big toe on his right foot in last Sunday's loss to Minnesota, was limited to 50 yards on 12 carries for Detroit.
The Lions scored the game's final 12 points, all on Jason Hanson field goals, but suffered their 20th straight road loss to the Packers. That streak includes a 1994 playoff game and eight Lions head coaches. Detroit's last road victory against the Packers came December 15, 1991.
Hanson split the uprights from 49 yards away 1 1/2 minutes into the fourth for a 28-23 margin and then Nelson suffered his second lost fumble of the day on the ensuing kickoff return. Stefan Logan recovered for Detroit at the Green Bay 18 and the Lions had a 1st-and-goal from the six, but they couldn't advance further. A third down pass to tight end Tony Scheffler went awry in the back of the end zone and Hanson made a 24-yard kick with 11:51 to play.
Another turnover by Green Bay gave Detroit an opportunity to go ahead. Alphonso Smith took the ball away from Greg Jennings on a deep pass. The interception gave the Lions the ball at their 29, but after a pair of first downs and facing a 4th-and-9 at the Green Bay 37, Detroit punted.
The Lions never got the ball back. John Kuhn rushed off left guards for a five-yard gain, giving the Packers a first down at the Detroit 39 at the two- minute warning. Rodgers then hit tight end Donald Lee with a 15-yard pass and Kuhn delivered the final blow, powering up the middle for eight yards on a 3rd-and-7. One kneel down by Rodgers ended the game.
"I don't think with a win in the NFL there's a whole lot of luck involved," Rodgers said. "We didn't play very well on offense, which put our defense in some tough spots. They were on the field for a long time."
It took the Packers just four plays to punch the ball in for a score after the opening kickoff, as Rodgers threw 29 yards to Donald Driver, who beat cornerback Jonathan Wade in coverage to the left side of the end zone.
On Detroit's first possession, Hill took the Lions from their own 29 to the Green Bay 17, but on third down Best fell down on a short route and A.J. Hawk came up with the interception.
"We've just got to stop shooting ourselves in the foot with penalties and mistakes," Best said. "It's just self-inflicted wounds that kill us."
The Lions, though, tied the game in the opening minute of the second quarter when Hill passed to a wide open Johnson in the end zone for a 23-yard score.
Less than three minutes later, Best fumbled in the backfield after taking the ball from Hill. Ryan Pickett recovered for Green Bay and an unnecessary roughness penalty on Detroit offensive tackle Gosder Cherilus moved the ball to the 12. On 3rd-and-goal, Rodgers gunned a pass over the middle between defenders to Jermichael Finley for a 13-yard TD.
Rodgers found Driver for a 48-yard pass connection, and on the ensuing play the third-year starter made another great precision pass, lofting the ball over Wade and into the waiting arms of Jennings for a 17-yard score. That extended the margin to 21-7 with 6:48 left in the half.
Detroit ate up nearly all of the remaining time in the quarter, and on 3rd- and-goal from the 21, Johnson won a jump ball in the end zone between two defenders with eight seconds left.
Nelson fumbled the ensuing kickoff return, but Hanson was short on a 55-yard field goal try to conclude the half.
Just 26 seconds into the second half, Woodson dove for a poorly thrown pass to Johnson on the left side of the field and came up with the interception, taking it back for a score with little resistance. Detroit challenged the ruling but lost, giving Woodson his 10th interception return for a TD and a 28-14 cushion.
Hanson kicked a 39-yard field goal 5 1/2 minutes into the third quarter to get the Lions within 28-17.
Chris Houston then picked off Rodgers at the Detroit seven. The turnover came after the Packers recovered a Rodgers fumble and after another interception by Houston was nullified by an offsides call on the Lions. Detroit, though, turned the Green Bay miscue into another three points with Hanson connecting from 52-yards away with 1:43 left in the third.
Green Bay will play the Redskins next Sunday in the team's first trip to Washington since 2004, while the Lions return home to host the St. Louis Rams...Woodson is alone in third place in touchdowns via interception return, behind only Rod Woodson (12) and Darren Sharper (11)...Lions tight end Brandon Pettigrew caught eight passes for 91 yards...Packers rookie safety Morgan Burnett suffered a knee sprain.