Middlesbrough manager Steve McClaren predicted before this game that Newcastle had an outside chance of the Premier League title - provided that they won their final ten games.
This result effectively rules out any chance Newcastle have of catching title favourites Arsenal.
The Magpies' target now must be to challenge Manchester United for the runners-up spot.
Overall Boro deserved their success with Geremi, on loan from Real Madrid, the all-important goalscorer.
Amazingly, his header that beat Shay Given after 62 minutes, was the only effort on goal by either side in the entire game.
There were plenty shots at goal in a game that was often fast and furious but neither Mark Schwarzer nor Given had what could be termed a serious shot to save.
McClaren named Brazilian star Juninho in his starting line-up after a great deal of pre-match speculation.
Another injury victim, Ugo Ehiogu, was also in the side after a 45-minute substitute appearance.
Play was always fast and open with both sides going for a win. There was never any question of either side putting up the defensive shutters.
It was a measure of the quick tackling and covering of defences that the goalkeepers were not put under serious pressure.
Geremi became the hero of the home crowd when, from a cross by Franck Queudrue, he gave Given no chance with a header.
Newcastle lost the experienced Gary Speed through injury after 77 minutes.
Newcastle manager Bobby Robson sent on three substitutes in a bid to save the game but Middlesbrough were in no mood to throw away their lead.
"We looked a very good side tonight," McClaren said after the game. "We played very well against a side that is third in the table.
"Our back four were superb. I thought Newcastle's defence was almost as good as ours." Sir Bobby Robson said: "It was a very narrow defeat but on the night Middlesbrough were just that little better than us.
"We lost our way because we did not work the flanks enough. We tried to play through the middle and that played to their strengths."