Fields was timed at 20.33 mph on the play, not good enough to make him.
The top 20 for the year in the league but his run of 21.23 versus Dallas still stands in the top 10.
Bears quarterback Jay Cutler's 61-yard run on 16 November 1980, in a 10-6 defeat to the Houston Oilers.
A new franchise mark for longest run by a quarterback, surpassing Vince Evans' 58-yard effort from the previous season.
Last week, ESPN's Eric Moody recommended drafting Fields in fantasy leagues, and the next week against Miami.
Fields rewarded Moody's prediction with 42.7 fantasy points.