It took Palace just six minutes to penetrate the visitors’ nervy backline. Aki Riihilahti’s overhead kick found Danny Granville on the left and he in turn found Black.
His neat pass found Adebola who swept the ball in from close range low to Robert Green’s right.
Having made the first, Black then arrived at the end of a fine move to head the second on 27 minutes. Shaun Derry and Riihilahti combined to find Granville on the left again and the wing-back supplied a quality cross for Palace's in-form player.
Norwich are on a poor run of form away from home - this was their fifth straight defeat on their travels. They rarely troubled the home defence and were limited to long-range strikes, summed up by Clint Easton's tame speculative free-kick from 30 yards being their best effort all match.
Andy Johnson had the best chance of the second half, when sent through by Hayden Mullins on the hour, but shot well wide.