Stephen Ireland finished off a well-crafted move to put Man City 2-0 up at Everton in 2009.
Robinho had already handed the Blues the lead, and the Brazilian would set up the second as the visitors kept their hopes of Europa League qualification alive.
A sweeping counter-attack saw Felipe Caicedo find Robinho, who then delivered an excellent clipped ball to Ireland.
'Superman' kept a cool head, gathering the pass and slotting into the bottom corner.
Dan Gosling set up a nervy end with an injury-time strike for the hosts, but City hung on for a first win at Goodison Park in almost 17 years.