With the pre-match talk dominated by reports that Alan Pardew will take over at Palace, the Newcastle United boss watched on from the stands as both sides struggled in front of goal.
Yannick Bolasie squandered the best chance of the game, lashing an effort against the crossbar after breaking free of the home defence.
Villa had chances of their own, with Alan Hutton seeing an early attempt smothered and Christian Benteke blazing over midway through the second half, but the hosts could not capitalise on their dominance of possession.
Pardew will have been given food for thought by the toothless nature of Palace's attack and the London club - who remain in the bottom three - are now without an away goal in the league since November, while Villa have now only found the net once in their last five.
The hosts, who made three changes from the draw with Sunderland, had scored fewer goals this season than any other League team in England before Thursday's encounter, but they started brightly.
Some good build-up play within the first three minutes allowed Andreas Weimann to tee up Benteke inside the area and the Belgian forced a smart save from goalkeeper Julian Speroni.
Palace, without captain Mile Jedinak who is away on international duty with Australia, struggled to assert themselves and should have fallen behind after quarter of an hour.
A surging run from Aly Cissokho down the left allowed Hutton to be picked out inside the area, but his low effort was magnificently saved by Speroni.
Villa's star defender Ron Vlaar was then forced to limp off after a challenge with Damien Delaney, and the visitors nearly took advantage two minutes later.
Some individual brilliance saw Bolasie power past two defenders, before bursting into the penalty area and crashing a shot against the crossbar.
Leandro Bacuna curled a 30-yard free-kick just over the bar 10 minutes later as the hosts searched for a breakthrough, but both goalkeepers were left largely untroubled for the remainder of the half.
Tom Cleverley saw a shot deflected wide after 52 minutes, before Benteke headed off target a few moments later as Villa continued to press.
They had to be alert at the other end when a fortunate bounce allowed James McArthur to make space inside the area, only for the Scot to be denied by Cissokho's last-ditch tackle.
Benteke spurned another chance 18 minutes from time, firing over from inside the area following Carlos Sanchez's cutback, before Bacuna stung the palms of Speroni with a powerful free-kick on the edge of the area late on.
But Paul Lambert's side could not find a breakthough, drawing a blank for the 11th time this season.
