The hosts had the greater number of opportunities, striking the woodwork twice in quick succession during the first half, while Kenwyne Jones missed a presentable headed opportunity midway through the second period.
Villa struggled to create clear-cut goalscoring chances, Leandro Bacuna wasting their best position just after the hour when he sent a shot wide of goal after bursting through, while David Marshall made the save of the game in stoppage time, somehow tipping away substitute Andreas Weimann's close-range effort when he appeared to be moving in the wrong direction initially.
|By Tim Poole
Tuesday's result marks a worrying day for Cardiff City fans, with Ole Gunnar Solskjaer's side having picked up just four points from their last seven games.
The Bluebirds had two moments of brilliance in the first half, when Craig Noone and Fraizer Campbell hit the woodwork within seconds of each other. That, though, was all that they could boast as Aston Villa grew and grew into the game in the second half.
The hosts have David Marshall to thank for the fact that Villa did not take all three points, although Paul Lambert's side can also blame Gabriel Agbonlahor - with the forward being wasteful with his chances and offering very little in the final third.
The Bluebirds made four changes and the Villans three from their respective defeats on Saturday, with Craig Bellamy an enforced change for Ole Gunnar Solskjaer as he served the first of a three-match ban for striking Swansea City's Jonathan De Guzman.
Delph fired an early warning shot for Villa in the 10th minute, sending a low effort a yard wide of the left-hand post from just outside the area, but Cardiff responded brightly and struck the woodwork twice in the space of 30 seconds in the 14th minute.
First Wilfried Zaha played in Fraizer Campbell, whose effort from a tight angle was diverted onto the post by Brad Guzan, before Craig Noone cut inside from the right and his shot looped onto the crossbar via a wicked deflection off Ashley Westwood.
Cardiff appealed in vain for a penalty five minutes later when Jones appeared to be hauled down by Nathan Baker as he tried to reach the byeline but the remainder of the first half was largely without incident - Zaha's effort, disallowed for offside 10 minutes before the break, the closest that either side came to scoring.
Campbell wasted a good opportunity nine minutes after the restart, dragging his shot well wide of the target after creating space for himself on the edge of the box.
Villa have proved dangerous on the counterattack away from home all season and so it proved again in the 61st minute, Bacuna exchanging passes with Gabriel Agbonlahor before driving into the area and sending his effort narrowly wide of the left hand upright.
Jones was similarly wasteful five minutes later, planting a free header straight at Guzan from 12 yards, before Marshall flew to his left to deny Delph's deflected effort.
Agbonlahor ought to have won it for his side in the 82nd minute but took too long and allowed Kevin Theophile-Catherine to get back before Marshall made an incredible reaction save to deny Weimann in stoppage time as both sides had to settle for a point.