With Cardiff tiring badly, Emmanuel Adebayor wasted an inviting chance to settle the tie when he snatched at Robin van Persie's cross.
And Ross McCormack was unlucky with a dipping free kick which rattled Luis Fabianski's crossbar.
It took Arsenal 20 minutes to create a chance. Van Persie fed the ball through to Samir Nasri on the left of the box but Cardiff goalkeeper Peter Enckelman came off his line to make a vital block.
Emmanuel Eboue was booked for an embarrassing dive in the Cardiff area as Arsenal's frustration escalated.
The pace slowed after the break, but Cardiff – flying high in the Championship – still committed numbers to attack.
Arsenal scented an opener when they were awarded a free-kick 30 yards from goal. Van Persie hit it well, but the ball flew inches wide of Enckelman's right-hand post.
Enckelman had to dive to gather a chested pass from his left-back Mark Kennedy as again play switched from end to end.
Arsenal were the first to make a change, in the 59th minute when Abou Diaby came on for Aaron Ramsey.
And though their dominance increased as Cardiff faded, Adebayor's miss was the nearest Arsenal came.