Rodgers connected with receivers Ty Montgomery and James Jones for long scoring strikes.
But NFL-record streaks of 587 pass attempts and 49 touchdown passes at home without an interception for Rodgers ended in the first quarter on linebacker James Laurinaitis’ diving pick of a tipped ball for the Rams (2-3).
Rodgers threw another interception in the second quarter before losing a fumble in the third.
Relentless pressure on quarterback Nick Foles helped keep the Packers (5-0) unbeaten. Foles threw a career-worst four interceptions, two in the fourth quarter inside the Packers 10.