Giorgio Tavecchio also connected on a field goal as the Packers built a 12-0 lead early in the second half.
Rodgers finished with 134 passing yards and backup B.J. Coleman also fired a TD pass as Green Bay posted its first exhibition win after falling to Arizona in its opener last week.
St. Louis fell to 0-2 in the pre-season after Sam Bradford was held to just 8-for-12 efficiency for 155 yards.
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