Villa may be the only unbeaten team in the Premiership, but there were plenty of warning signs for manager Martin O'Neill to take on board.
Fulham, who last beat Villa in the top flight at Villa Park as long ago as 1966, maintained a self-belief which eventually earned them a well deserved point.
Villa skipper, Gareth Barry, meanwhile boosted his international recall in front of England manager Steve McClaren with another impressive performance which he capped with his explosive first-half penalty.
The enforced absence of Gavin McCann was an early blow to Villa who had to re-organise their defence with Martin Laursen, making only his third start of the season, giving a masterly display.
But with Stilian Petrov taking firm control of the midfield Villa always had an edge on the general play in a first half which should have seen them build up a commanding lead.
Their newly acquired confidence was a major feature of the latest performance which was largely generated by Petrov and Barry.
The only disturbing feature was again the Juan Pablo Angel-Milan Baros partnership which again struggled to make an impact despite an immaculate service from the likes of Gabby Agbonlahor.
In the early stages both players carelessly wasted gilt-edged opportunities which would have seriously demoralised Fulham who eventually found themselves in familiar circumstances when they went a goal down.
Fulham really had no excuse as they were somewhat fortunate when both Liam Ridgewell and Angel failed to make connection only yards away from goal.
Villa's steam-roller tactics forced Fulham on to the defensive with Zat Knight and Ian Pearce both in commanding form to keep the Londoners into he game.
But in the 24th minute Villa's superiority paid off. Liam Rosenior had been involved in a running battle with Petrov from the opening whistle and on this occasion he impeded the Bulgarian and conceded a penalty.
After his bad miss against Spurs in the previous home game Angel was not given the responsibility of taking the spot-kick. On this occasion the responsibility fell on the shoulders of skipper Barry, who blasted the ball past Antti Niemi.
Fulham's response was a Brian McBride inspired raid. The American's shot was slightly off target but went straight to Claus Jensen who conspired to fumble his close-range attempt straight into the arms of Thomas Sorensen.
But Fulham lived up to their reputation as the comeback specialists by snatching a vital 43rd minute equaliser in clinical fashion.
Tomasz Radzinski produced the left-wing cross which was guided into the net by Moritz Volz for the German's first goal of the season after Ridgewell had been sucked into a central defensive role and Barry had not back-tracked quick enough to shut out the Fulham defender.
The second half was an untidy affair as Villa went off the boil after Ridgewell, Laursen and Mellberg all missed a free kick from Barry.
In this period Villa drafted in the two former Celtic players, Didier Agatha and Chris Sutton, but they could not make an immediate impact, while 19-year-old unknown Isaiah Osbourne also made his first appearance in what was a disappointing result for Villa.