After a quiet opening half hour, Fernando broke the deadlock after 34 minutes when he headed in from Jesus Navas’ corner.
Aguero doubled the lead before half-time from the penalty spot after Shawcross fouled Iheanacho.
Joselu, Mame Biram Diouf and Marko Arnautovic all went close for Stoke early in the second half.
But Iheanacho wrapped up the win just after the hour mark with a composed finish after receiving Pablo Zabaleta’s pass.
He added his second of the game in the 74 minute when he rounded substitute goalkeeper Jakob Haugaard to finish into an empty net.