The victory means that the Jets no longer have the first team in next year's draft, which is now instead with the Jacksonville Jaguars.
They have the same result (1-13), but have had easier resistance.
Two rounds remain of the basic series.
Next year's draft is seen as extra important as 21-year-old quarterback Trevor Lawrence, the Clemson Tigers, is seen as the greatest talent in American football in several years.
- Hey, our job is to go out and win matches, says coach Adam Gase, who does not think a loss would have been more beneficial for the club.
The Jets' victory over the Rams is one of the biggest bangs in the NFL this season, but thus puts sticks in the wheel for their long hunt for a quarterback star.
The suite of 13 straight losses is the longest in the club's history.
Only two teams in NFL history have lost all 16 regular season games.