The Villans stay near the Premier League drop zone after creating plenty of chances but, once again, failing to make their dominance count against the below-par London side
The first half was played at a good tempo, with the home side creating some good chances as the superbly restricted Martin Jol's side.
The Villans took the lead thanks to Charles N’Zogbia, although Fabian Delph’s own goal just 10 minutes later prevented them from taking all three points.
Villa manager Paul Lambert made one change to the side that beat Stoke, with N’Zogbia coming in for the injured Gabriel Agbonlahor.
Meanwhile, Jol made two changes for the Cottagers, bringing in Kieran Richardson and Urby Emanuelson for John Arne Riise and Stanislav Manolev.
Both sides began the game brightly and at a good tempo, although Damien Duff was forced off in the opening 10 minutes for the visitors after suffering a groin injury.
The first chance of the game fell to Villa in the 24th minute as Christian Benteke found himself unmarked five yards out but put his shot over the bar.
The home side then saw Andreas Weimann nearly reach a Jordan Bowery pass but for the intervention of Mark Schwarzer after confusion in the Fulham defence.
Moments later, Benteke played a superb pass into the box from the left to find N’Zogbia, whose half-volley was hammered on target but saved brilliantly by Schwarzer.
The Villans were nearly punished for their wastefulness after 42 minutes, as Dimitar Berbatov took down a pass, but saw his lashed shot blocked away for a corner.
Schwarzer was called into action once again by a stinging N’Zogbia shot in the 44th minute, which he palmed away for a corner to keep the game scoreless at half-time.
The second half began similarly and within 15 seconds of the restart Weimann ploughed forward, with his placed shot forcing Schwarzer to make a good low save.
Just five minutes later Villa were nearly punished as Berbatov was played through but could only direct his shot onto the outside of the post in Fulham’s best chance of the game.
The home side were finally rewarded in the 55th minute as the ball broke to N’Zogbia after some good work by Weimann and the Frenchman brilliantly curled his shot into the net.
Going behind seemed to galvanise Fulham, and they equalised in the 65th minute as a Bryan Ruiz corner was turned into his own net by Delph at the near post.
And the Cottagers nearly took the lead just five minutes later as Ruiz found substitute Mladen Petric, but he could not direct his close-range shot on target under pressure from Matthew Lowton.
Delph then had a chance to atone for his earlier own goal in the 73rd minute as he found himself free at the back post but hammered his shot well over the bar.
However, neither side could create any more clear chances in the final stages and had to settle for a point.