Fulham's first victory in eight games kept them 13th in the standings, three points and one place ahead of Newcastle.
Steve Sidwell put Fulham ahead with a deflected shot after 19 minutes, their first goal in over five hours of Premier League action.
Newcastle equalised through a brilliant 20-metre strike by midfielder Hatem Ben Arfa which flew into the net off the underside of the crossbar early in the second half.
Rodallega rose to head home Damien Duff's free kick after 63 minutes although Newcastle almost levelled again when Fabricio Coloccini's powerful shot struck the crossbar. (Reporting by Ed Osmond, editing by Ken Ferris)