One of Crosby's efforts was a season-high 52-yarder field goal with 11:19 left in the first half.
Rodgers completed 20-for-30 passes for 274 yards with an 83-yard touchdown toss to James Jones for the Packers (2-2), who bounced back following a loss to Cincinnati two weeks ago.
Jones ended with 127 yards on four grabs and Eddie Lacy added 99 rushing yards on 23 carries as Green Bay won its 23rd straight home game against NFC North rivals Detroit.
The Lions (3-2) stumbled offensively as Matthew Stafford was held to 262 passing yards with a score on 25-for-40 efficiency.
Star wide receiver Calvin Johnson sat out the game with a knee injury.