The Packers celebrated the achievement on Twitter:
Rodgers reached the milestone in his 144th appearance. He hit Ty Montgomery for a one-yard touchdown pass with his 43rd passing attempt Sunday night, which was his 4,742nd career attempt, making him the fastest quarterback to throw 300 touchdowns.
Moving further up the all-time leaderboard won't be easy for Rodgers since active players (Ben Roethlisberger, Eli Manning and Rivers) hold the next three spots. Fran Tarkenton is the next retired player on the list and sits sixth with 342 touchdowns.
Manning owns the gold standard with regard to passing touchdowns. He closed the curtain on his NFL career after compiling 539 touchdowns through the air.
Since replacing Brett Favre as the Packers' starting quarterback in 2008, Rodgers has averaged a little under 2.2 touchdowns per game. If he maintains that pace, he'll need to make roughly 110 more appearances in order to catch Manning and take over the top spot.