Yakubu, fit again after his recent heel injury, had a glorious chance to level five minutes after the goal when he ran on to Saha's flick-on, only to be denied by an excellent Ross Turnbull save, while Lescott came closer still when his clipped cross floated over the keeper's head and hit the post.
Tuncay and Afonso Alves were causing plenty of problems on the counter at the other end, but it was Everton creating the better chances and Boro were fortunate when Yakubu went down under Turnbull's challenge, only for referee Howard Webb to wave away the penalty appeals.
And when Cahill rose to meet a corner completely unmarked eight yards only to head wide, one wondered if the hosts may live to regret their profligacy.
Southgate satisfied with away point
However, Everton fans need not have worried, with their equaliser coming soon after the hour mark, ironically during Boro's best spell of possession in the match.
Minutes after Saha had sent a crashing diving header wide from a flowing Everton move, former Middlesbrough striker Yakubu levelled when he got the decisive touch on Arteta's free-kick from six yards out.
Boro looked for an immediate response and very nearly got one when Didier Digard curled goalwards from 20 yards, keeper Tim Howard pushing the effort on to the post.
But it was Everton who went closest to a winner when Yakubu found himself free in the box, only to send his drive across goal and away for a goal kick.
Despite a late flurry from both sides, neither could muster a winner - as David Moyes marked his 250th game in charge of the hosts with a draw.
Everton manager David Moyes: "We missed a lot of opportunities and have played better. When they went ahead with a goal on the counter-attack there was always the chance that they could do that again, so we needed to be careful.
"But give us credit, we kept going forward although we found it very difficult to score.
"I was pleased for Yakubu to have scored. He had a couple of other chances beforehand so he will be pleased with his effort too. He did a lot better in this one, overall it was a better performance from him."
Middlesbrough boss Gareth Southgate: "We played very well in the first half but we needed a second goal in that spell to see us through.
"We did well on the break, but we didn't pass the ball well enough. We showed some different characteristic in this one, we had to roll our sleeves up and defend the box. We are young and we are learning.
"But we have taken eight points from our last four away games and we are unbeaten in five since losing to Chelsea. That is as good a run as anyone else in the division."
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