Detroit (2-3) earned a win it desperately needed under first-year coach Matt Patricia, going into its bye week.
Crosby missed a career-high four field goals in one game and missed an extra point to boot.
He connected on a field goal with 2 seconds left. Detroit recovered the onside kick to seal the win, preventing Rodgers from getting another chance at a game-winning Hail Mary in Detroit.
Blount had a pair of 1-yard TD runs in the first quarter and Stafford's 8-yard pass to Marvin Jones late in the second quarter put Detroit up 24-0.
Stafford answered with a 5-yard TD pass to Kenny Golladay early in the fourth quarter to give Detroit a 31-14 lead.
Rodgers connected with Davante Adams on a 12-yard throw for a third TD pass, but Crosby hit the left upright on the extra point to let the Lions keep an 11-point cushion midway through the fourth quarter. Adams has scored in 10 straight road games, equaling a league record set by Tommy McDonald of the Philadelphia Eagles from 1959 to 1961.
Rodgers was 32 of 52 for 442 yards with three TD passes. Stafford was 14 of 26 for 183 yards with two TDs and no turnovers.
Lions: RB Kerryon Johnson, who ran for 70 yards on 12 carries, went out in the fourth quarter after appearing to hurt his right ankle. CB Teez Tabor (groin) and CB Jamal Agnew (knee) also left the game with injuries.
Packers: Host San Francisco on Monday, Oct. 15.
Lions: Off until playing at Miami on Oct. 21.
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