Cook, 17, threw himself to his right to brilliant turn behind Manchester City's Ishmael Miller's 63rd minute spot kick after referee Dave Richardson controversially penalised Paul Huntington for what looked to be a clean challenge on Miller just inside the box.
Michael Chopra gave United a 19th minute lead. Chasing a long ball from Kris Gate, he was beaten to the ball by centre-back Nathan D'Laryea. But the defender's clearance ricocheted off Chopra and bounced past the advancing Belgian goalkeeper Geert de Vlieger.
But Miller pulled City level, firing across Cook from eight yards following a through ball from Wright-Phillips on 33 minutes.
NEWCASTLE UNITED: Cook, Shanks, Cave, Atkin, Huntington, Gate, Brittain (Cavener, 72), Pattison, Finnigan (Trouisi, 77), Chopra (Carroll, 67), O'Brien.
Subs Not Used: Reay.