Midway through the first half, as play continued, an announcement was made over the public address system to Cardiff fans urging them to desist from alleged racist and homophobic chanting that was deemed "not acceptable".
Reading were reduced to 10 men in the 81st minute when centre back Tom McIntyre was dismissed for collecting a second yellow card.
Both sides had reached round four with replay victories – Reading 2-0 at League One Blackpool, Cardiff 4-3 at League Two Carlisle.
Two goals in the opening eight minutes got the tie off to a hectic start.
Cardiff went ahead in the fifth minute, when Meite clumsily lost possession in midfield.
Joe Ralls crossed to the far post, Aden Flint nodded it goalwards and Paterson pounced from close range.
Reading thought that they had gone in front in the 35th minute after Smithies failed to hold a powerful shot from Sone Aluko.
Meite tucked home the loose ball but was ruled offside.
Reading began the second period strongly, with Andy Rinomhota having a shot blocked on the edge of the Cardiff area.
Play was then held up for several minutes as Reading captain Matt Miazga received treatment for what appeared to be a leg injury.
He was eventually carried off on a stretcher and replaced by Gabriel Osho.
Cardiff upped the tempo afterwards and Bamba went close with an audacious back flick from a Gavin Whyte cross.
Walker was also forced to make a smart point-blank save from Glatzel.
McIntyre saw red nine minutes from time for a rash tackle on Paterson then Bamba, in the frantic closing stages, somehow headed wide with the goal at his mercy.