Leon Osman tapped in Everton's fourth from close range after Johnny Heitinga's free-kick came off the wall.
But Everton were clearly in control and Osman compounded Hull's misery by pouncing after Heitinga's free-kick was not cleared.
That has left boss David Moyes short of options, with new signing Heitinga ineligible until January to play in Europe.
Portsmouth had a shout for a penalty waved away by referee Alan Whiley when Kevin-Prince Boateng felt he was impeded by John Heitinga.
Heitinga somehow contrived to head wide from Seamus Coleman's far-post cross.
Everton, whose lengthy injury list looks likely to grow after Johnny Heitinga limped off, had looked more likely to extend their lead than be pegged back.
Sylvain Distin and Phil Jagielka marshalled Everton's defensive unit superbly throughout, pressing and closing City's forwards, while Johnny Heitinga was effective in breaking down the supply line.
Spain had great chances in the second half with David Villa denied by the legs of Heitinga, and Sergio Ramos who headed over with the goal at his mercy.
Johnny Heitinga's driven pass was taken down superbly by Guerrero Antonio Lopez, who then picked out Maxi for an emphatic finish after his first touch took him past Jamie Carragher.
It meant an entire team was unavailable - nine out injured and two Cup-tied in Johnny Heitinga and Lucas Neill - so Moyes had a threadbare, inexperienced squad at his disposal.
Everton boss David Moyes, who fielded new signings Distin and Russia winger Diniyar Bilyaletdinov, later revealed the club have agreed a fee with Spanish side Atletico Madrid for defender Johnny Heitinga.
Referee Webb also comes under criticism for failing to act tougher as he handed out a string of yellow cards without using the ultimate sanction until Heitinga was sent off deep into extra-time.
With Johnny Heitinga cup-tied and Sylvain Distin suspended, Everton had a new central defensive partnership in Yobo and Philippe Senderos - and the latter was very harshly penalised for a foul on Yannick Djalo.
Everton belatedly showed the passion their play had been missing in the second half and they were rewarded when Zayatte swung at a Johnny Heitinga cross only to slice the ball into his own net.
Neill, who also held talks with Atletico Madrid of Spain and was linked with a move to Turkey's Galatasaray, is the fourth permanent addition to boss David Moyes' squad, following Sylvain Distin, Diniyar Bilyaletdinov and John Heitinga to Goodison Park.
However, Euro 2008 champions Spain, who conceded only two goals during the tournament, deserved their victory after gradually taking a grip on a tense and bad-tempered contest that produced 14 yellow cards with Johnny Heitinga sent off on 109 minutes after picking up a second yellow card.
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