The second successive victory took them out of the relegation zone and two points ahead of West Ham.
Yet it looked as if they had blown their chance after a string of misses, a header that hit the post and some brilliant saves by Spurs keeper Kasey Keller.
He was finally beaten in the 92nd minute when Youri Djorkaeff went down under Gary Doherty's tackle and referee Graham Poll pointed immediately to the spot.
Okocha, who has dedicated his stay in England to help Wanderers' survival bid, took the spot-kick, putting it inside the right-hand post and just out of reach of Keller's despairing dive.
The Londoners should have gone ahead in the 35th minute when Goran Bunjevcevic came out of a goalmouth melee to shoot at goal only to see Per Frandsen block the effort inside the six-yard box.
All that resulted in Wanderers launching high-speed attacks on the break and they almost capitalised when Henrik Pedersen got to the byline before crossing into the area where Keller was alert enough to knock the ball away from the run of the approaching Djorkaeff.
The pattern changed somewhat in the second half as Wanderers started to gain some measure of control in midfield.
And that enabled them to put pressure on a Spurs defence that was grateful for some touches of good fortune.
That was certainly true when Gudni Bergsson climbed to send a thundering header crashing against a post with Keller beaten.
And the keeper was grateful to see Pedersen put the ball narrowly wide as Wanderers increased the attacking tempo.
And they would have gone ahead had Keller not made a number of fine saves with Okocha just missing a headed chance.
He looked to have had the goal at his mercy when a blocked Anthony Barness shot rebounded to him, but the Nigerian only succeeded in heading over the bar from six yards out.
Other than that Spurs were saved by Keller. He tipped a Djorkaeff shot over the bar, bravely dived at the feet of Bernard Mendy before palming away a goalbound shot from substitute Pierre-Yves Andre.
Yet for all that Keller was finally beaten by the accuracy and pace of Okocha's spot-kick, diving the right way but failing to reach the well-directed shot.