However Hull looked the more dangerous side and Marlon King curled a free-kick just past the far post from the edge of the area.
Everton were finding it hard to break down the home defence and were restricted to half-chances as the hosts ended the first half in control.
David Moyes changed things round at half-time - bringing on Saha for his debut and Joleon Lescott, who had been dropped to the bench, for Segundo Castillo and Leighton Baines.
And Saha almost made an immediate impact as he and Yakubu pounced on the ball from a corner but keeper Myhill bravely blocked.
That save proved crucial two minutes later as Hull doubled their lead from another left-wing Marney corner.
Michael Turner scored his first goal in the Premier League to put Hull in front
The ball was delivered into the six-yard box and flew into the net for an own goal off a combination of the back of Neville's head and Howard's hand.
The goal seemed to ignite Everton and the visitors finally came into the game.
On the hour mark Saha had another chance as he burst into the area only to be denied by a smart save from Myhill.
Fellow substitute Lescott drove over soon afterwards and Everton's improvement was rewarded when Cahill pulled one back in the 73rd minute.
The ball pinged around the penalty area with Hull failing to clear and the midfielder's shot bounced down off the bar and over the line with the linesman awarding the goal.
Interview: David Moyes
The Toffees continued to attack and Hull again failed to get the ball away at a corner before it bounced into the grateful arms of Myhill.
However Myhill was powerless to stop the 78th minute equaliser as Osman poked the ball home from close range after Yakubu exchanged passes with Saha before crossing from the left-hand side of the penalty area.
Then Saha could only find the side-netting from a tight angle after Myhill dropped a centre.
The point maintained Everton's unbeaten away record and continued Hull's good start to their first season in the top flight.
Hull manager Phil Brown: "In the first half we played some of our best football of the season but to be fair without Lescott and Saha, Everton weren't as potent a threat as they were in the second half when they looked a totally different team.
"Beforehand we probably would have taken a draw but when you are 2-0 up after 65 or 70 minutes you are looking to close out the game.
"I've seen their first goal on video and it is not conclusive but it has to be the linesman's decision and he flagged for it going over the line.
"We now have eight points from five games and if we continue in that mode we will be all right."
Everton manager David Moyes: "I was disappointed we were two goals down but I don't think we should have got into that situation and credit to Hull for that.
"I thought that even in the first half we had more of the ball but didn't do anything with it but the introduction of Louis Saha made the difference.
"Saha is a very talented player and if we can keep him fit and out on the pitch he will be a big player for us.
"I have to credit the players who showed a lot of character to come back but people who have been very reliable for us have become unreliable. We must put an end to the goals and we are conceding from set-pieces."
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