Jay Rodriguez hoped to have set up Albion for just a fourth alliance triumph of the season when he spun to snare in Salomon Rondon's descending header ahead of schedule in the second half.
In any case, Alan Pardew's side lost their fixation in the midst of a guarded reshuffle following the substitution of chief Jonny Evans.
Jordon Ibe exploited as he slice in from the left to bob a shot past guardian Ben Foster from 25 yards.
At that point, Stanislas, who had been off-focus with several free-kicks from a comparative separation prior to the match, coasted an ideal shot over the divider and inside the post from the edge of the territory