Rivers, 38, entered the game in Nashville, Tennessee, with 61,358 passing yards in his 17-year career, needing just 4 yards to pass Marino. He finished the night 29-for-39 passing for 308 yards, putting him at 61,666 yards for his career. The Colts won 34-17.
The only other quarterbacks with more passing yards than Rivers are either in the Hall of Fame or will be first-ballot Hall of Famers at some point: Brett Favre, Peyton Manning, Tom Brady and record-holder Drew Brees.
Rivers has some work to do to surpass Favre, who threw for 71,838 yards in his career, for fourth place.
Thursday night marked another career milestone this season for Rivers, who signed a one-year, $25 million contract with the Colts during the offseason. In Week 3 against the New York Jets, he became just the sixth quarterback in league history to throw 400 career touchdown passes and for at least 60,000 passing yards for a career.