Fulham's first victory in eight games kept them 13th in the standings after 16 games, 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.
"That was vital for us," Fulham manager Martin Jol told Sky Sports. "I was so happy that we could score the first goal because that's been our problem in the last couple of weeks.
"I felt that we showed some character but I felt we should have finished it off early."
Newcastle, who beat Wigan Athletic last time out to end a run of four league defeats in a row, equalised through a brilliant dipping 20-metre strike by midfielder Hatem Ben Arfa which flew into the net off the bar 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.
"It's a really soft second goal," Newcastle manager Alan Pardew said. "Soft defensively on the free-kick and you can't do that at this level.
"We had the game by the scruff of the neck at that point. We played some of the best attacking football of the season but we still come away with nothing," he added. "In the second half we were terrific, other than two or three moments."
Manchester United beat champions Manchester City 3-2 in a dramatic derby on Sunday to open up a six-point lead over their local rivals at the top approaching the halfway point in the season.
