Hull had gone into the match without Jimmy Bullard as boss Phil Brown decided to rest his star man so that the midfield playmaker could recover from a minor knock to his knee.
Bullard has had a major impact for the Tigers since his recovery from a lengthy spell out injured but Brown was taking the longer term view when leaving him out and the home side initially made light of his absence.
Hull went ahead after Everton defenders Sylvain Distin and Leighton Baines missed a deflected Hunt cross to allow Altidore to hammer a point-blank shot, which Howard did well to fend away.
Brown pleased to win thriller against Everton
But Hunt had drifted in from the left and, with the Toffees defence sleeping, pounced to lash in the loose ball from eight yards.
The goal lifted Hull, while having the reverse effect on the visitors and the Tigers capitalised by extending their lead through Dawson's precise 25-yard free-kick into the top corner.
Everton had beaten Hull 4-0 at the KC Stadium in the Carling Cup earlier this season but were a different proposition this time around as they looked a team sapped of belief and confidence.
Too many of their passes were going astray, there was a lack of movement and, most unusually for the Merseysiders, they lacked fight.
A Baines corner was headed just over by Distin in a rare moment of threat from Everton but they soon found themselves further behind.
Distin inadvertently diverted a low cross to Marney and, symbolic of Everton's fortunes, the Hull midfielder's shot went in off Tim Cahill.
First-half display disappoints Moyes
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.
Zayatte was also involved in Everton's second goal as he was punished for a high challenge on Saha, who had expertly taken down a diagonal ball from Cahill in the box.
Saha dispatched the penalty with ease to set up a jittery finale for Hull.
Richard Garcia had a shot saved by Howard, while Cahill sent a long range strike over at the other end as more goals looked on the cards.
However, Hull had enough grit to hold Everton at arm's length and notch their fourth home win of the Premier League season.
Hull City boss Phil Brown: "I think it was a deserved win, even though Everton scored two goals in the second half. People might have been nervous at 3-2 but I wasn't unduly worried, I thought we still had a grip on the game.
"Defensively, we were very good in the first half. The second half was a different ball game and an own goal unhinges you to a certain extent.
"But we stuck at the task and thoroughly deserved the victory.
"Jimmy Bullard's in a new area of his rehabilitation. It was just a precautionary resting and fortunately it has worked for everybody.
"It now gives me a bit of a headache for Saturday, but they are the kind of headaches you want."
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