The result means that Cardiff remain several points adrift of safety, although it could have been worse as David Marshall made a string of second-half saves.
Stoke improved as the half wore on and threatened on the counter-attack through Peter Odemwingie and Stephen Ireland. They then started to control the game before being given a great chance to take the lead from the penalty spot.
Shortly after half time Webb levelled the penalty count. Frazier Campbell just got to the ball ahead of Steven Nzonzi and was subsequently brought down. Peter Whittingham took the spot kick and fired straight down the middle as Asmir Begovic dived.
Moments later the hosts thought that they had taken the lead. Begovic saved twice from Steven Caulker before Cala nodded the ball in from close range, only to be denied by the assistant referee's flag.
Both teams defended resolutely after that as Stoke quietened the home crowd and took the sting out of the game, before almost nicking all three points in the closing minutes as Odemwingie cut in from the right and saw his effort tipped wide by Marshall.
Marshall made another important stop in the final minute before Jonathan Walters hit the cross as Cardiff hung on for a point.