Stoke have been one of the form teams of 2004, but were relieved that Asaba ended a drought in front of goal to earn them the points.
Darel Russell had scored against the run of play to give the hosts the lead - smashing home after good work from Gifton Noel-Williams.
The Saddlers levelled through Jorge Leitao, heading home from an exquisite chipped pass by Paul Merson.
Asaba's first re-established the home side's lead on 37, finishing with aplomb after being set up by Kris Common.
Three minutes before the break it was all square when Kris Taylor guided home.
However, Noel-Williams capped a fine performance when he escaped down the wing and laying on a perfect cross for Asaba to grab the winner.
