The 20-year-old illustrated why with another all-action performance in the third-round tie against the Potters.
A late challenge from Ryan Shotton - missed by referee Neil Swarbrick - brought a premature end to Zaha's afternoon, but Stoke boss Pulis had already seen enough.
"He looks a terrific player," said Pulis.
"He's got great feet and his balance, like all great players, is wonderful.
"He can go either side and he shifts people without even touching the ball. He's a top, top player."