But Jones allayed any fears of a move south as has agreed a new deal which will keep him on Wearside for another four-and-a-half years.
And to put the icing on the cake, the Trinidad & Tobago international netted his seventh goal of the season to ensure his side took the spoils.
To be fai,r the hosts just about edged it in a game where neither side really shone.
Despite slim offerings in terms of flair football, there were chances for both sides.
Djibril Cisse went close to opening the scoring for the Black Cats on seven minutes. A clever ball down the flanks from Steed Malbranque set the pacey forward on his way but his shot was wide of the mark.
The Frenchman went closer on 27 minutes as Jones played him in on the edge of the 18-yard area, but Fulham keeper Mark Schwarzer managed to palm away his powerful drive.
Both strikers found their way to goal blocked on 36 minutes. Jones picked up a loose ball and rode a tackle before firing in a shot which was blocked by Schwarzer.
The ball came back out to Cisse whose attempt was charged down by a last-ditch tackle from John Paintsil.
Fulham weren't without chances of their own with Clint Dempsey firing wide after being put in by Andy Johnson in the 39th minute and Simon Davies volleyed wide four minutes later as the half came to a close.
After the break it was more of the same and you wondered if either side would find the cutting edge needed to make the breakthrough.
With the hour mark approaching it was that man Jones who answered in the affirmative.
Andy Reid took the attack to the visitors before being tackled on the edge of the area by former Sunderland man Dickson Etuhu.
The ball fell invitingly for Cisse and he shot at goal only to see Schwarzer deny him once more, but the ball came back to Jones and he fired home.
Malbranque tried to double the lead on 62 minutes but Schwarzer got down well to save his driven effort.
Six minutes later, Fulham had a gilt-edged chance to get back on level terms as Dempsey headed back across goal and Davies somehow managed to poke over the bar from just a yard out.
As the clock ran down, the Londoners pressed, desperately seeking an equaliser, but the hosts hung on to make sure a much needed victory was theirs.