Green Bay's 19th straight win -- the second longest streak in NFL history -- was blemished when Greg Jennings went down with a knee injury in the third quarter. Jennings was tackled by a pair of Raiders defenders after making a catch along the right hash mark, and one fell directly on the back of the star wide receiver's left knee.
Jennings was visibly shaken after the incident and was carted to the locker room after a visit with team trainers on the sideline.
The injury cast a shadow over the NFC North-champion Packers becoming the second defending Super Bowl champion to start the following season 13-0.
Rodgers threw for 281 yards with an interception on 17-of-30 passing in less than three quarters, while Grant added 85 yards on 10 carries.
Carson Palmer was intercepted four times for the Raiders (7-6), who fell one game behind the AFC West-leading Broncos. Palmer threw a late touchdown pass and had 245 yards on 24-of-42 throws.
The rout started early, with D.J. Smith picking off Palmer in Packers territory on the game's opening possession.
Two plays later, Grant broke through the line of scrimmage on the left side and went 47 yards for his first touchdown since 2009.
Later in the opening quarter, Green Bay's 10-play, 80-yard drive ended with Ryan Taylor making his first career catch, a four-yard grab just past the goal line.
Crosby tacked on a 34-yard field goal early in the second quarter, and Rodgers connected with Jordy Nelson on a 37-yard touchdown with 9:14 left in the half.
Following another Palmer interception -- hauled in by former Raider Charles Woodson -- Grant went in from six yards out for a 31-0 cushion heading to the break.
Jennings was injured on the first drive of the second half, which resulted in Crosby's 38-yard field goal.
Michael Bush got Oakland on the scoreboard with a two-yard TD run, but after another Crosby field goal, Raiders fullback Marcel Reece fumbled and Erik Walden returned the loose ball five yards for a Green Bay touchdown.
Crosby's 33-yard field goal early in the fourth capped the Packers' scoring.
The Patriots hold the longest NFL winning streak at 21 from 2003-04...Denver is the only other Super Bowl winner to start the next season 13-0, doing so in 1998...Rodgers has at least two touchdown passes in every game this season, though his streak of 12 straight games with a 100-plus QB rating came to an end (96.7)...Nelson had 81 yards on three receptions, while Donald Driver added 75 yards on four catches...The Packers play at Kansas City next week before hosting division rivals Chicago and Detroit to close out the regular season games...Bush totaled 78 yards on 23 carries...The replay system malfunctioned when the Raiders attempted to review whether Randall Cobb stepped out of bounds on the second-half kickoff.