They were in control for most of the game against a disappointing Manchester City side and could even afford to miss a first half penalty as well.
The Trotters could have been a couple of goals in front inside the first half hour.
There were clear-cut chances for Bernard Mendy and Pedersen that forced good saves from Peter Schmeichel while the home side also had three strong penalty claims.
The first two were turned down but when Schmeichel brought down Youri Djorkaeff in the 22nd minute, referee Clive Wilkes pointed immediately to the spot.
It was a decision Schmeichel strongly protested about and in the end it cost him a yellow card but when Okocha tried to fox the Danish keeper, he only succeeded in putting the penalty wide.
That however, only served to fire up the Wanderers and Okocha in particular, and it was his storming run down the left and cross that left Henrik Pedersen with a simple tap in to beat Schmeichel after 32 minutes.
Another dazzling piece of skill by the Nigerian saw him flash a shot past the far post but City did have their moments, especially when Nicolas Anelka blazed over the bar from close range after coming under close attention from Gudni Bergsson.
City found no room for improvement after the break as Wanderers continued to turn the screw, especially in midfield.
The Maine Road men, beaten 5-0 at Chelsea on their last outing, struggled to match the work rate and inventiveness of the home side and it was no surprise when Wanderers increased their lead seven minutes into the second half.
This time it was set piece play from a corner, Djorkaeff putting the ball to the near post when Ivan Campo rose unchallenged to power a downward header past Schmeichel's despairing dive.
Keegan's answer to that was to put on all three of his substitutes, but it had no effect on the game as City were unable to raise their game to put any kind of pressure on the home side's defence, in which central pairing Bergsson and Florent Laville were outstanding.