Powell finished with 42 yards on 11 carries while the Jets forced five punts and scored 14 points off of three turnovers.
Mark Sanchez completed 15-of-20 passes for 178 yards with a touchdown pass to Chaz Schilens for New York (4-6), which shook off last week's loss to Seattle.
Shonn Greene ran for 64 yards on 18 carries for the Jets.
Sam Bradford threw two TD passes but managed to complete just 23-of-44 passes for 170 yards with an interception and lost a fumble for the Rams (3-6-1).
Puzzle-maker slips 'Murdoch Is Evil' into Rupert Murdoch's Sunday Telegraph
Wisconsin business offering 'therapeutic cuddling' forced to close