Rogers finished with a pair of scoring strikes, going 19-of-27 through the air for 236 yards with an interception as the Packers (7-3) erased a late 20-14 deficit and racked up their fifth straight victory.
Jermichael Finley caught a TD pass and James Starks ran for 74 yards on 25 carries.
Green Bay improved to 2-0 in the NFC North and 7-3 overall.
The Lions (4-6) fell to 0-4 in divisional play as Matthew Stafford was held to 17-for-39 passing for 262 yards with a touchdown, two interceptions and a lost fumble.
Calvin Johnson made five grabs for 139 yards and a touchdown for Detroit.