The Giants' first-round pick in the 2014 NFL draft reached 3,500 yards in 36 career games.
San Diego Chargers legend Lance Alworth previously held the record, as he reached 3,500 yards in 37 career games.
Beckham scored a 10-yard touchdown later on the drive. The Pro Bowl receiver entered the season with the most receiving yards in his first two professional seasons. He had 2,755 yards despite missing five games in his first two seasons.
Beckham, 24, finished the game with 10 catches for 97 yards and a touchdown to give him 54 catches, 773 yards and six touchdowns in nine games this season.