Vick passed Randall Cunningham with a 53-yard, third-quarter scramble that gave him 4,946 career rushing yards, surpassing the former Eagles quarterback's league mark of 4,928. Cunningham needed 16 seasons to amass his total, but Vick broke the mark in just nine.
Coming into the game, Vick had rushed for 228 yards on 32 carries this season. He became the first player in history to throw for more than 400 yards and run for 75 yards in the same game last week against the San Francisco 49ers.
Vick set the NFL single-season quarterback rushing record with 1,039 yards in 2006, while he was with the Atlanta Falcons.
The Associated Press contributed to this report.