The Teesside club had to weather heavy pressure from the home side in the second half and will be happy to take a point back to the North East.
Hamilton Ricard (pictured) broke his dismal goalscoring record in the league from open play in the 11th minute to give Bryan Robson's men the lead.
However, a goalkeeping error by Mark Schwarzer handed Gary Naysmith the opportunity to level just four minutes into the second half, which he gratefully accepted.
The visitors re-took the lead from a similar situation, Thomas Myhre who had earlier in the day expressed his fear that he would be dropped for the game, produced a clanger that allowed Colin Cooper to loop a header into the unguarded net, his first goal since 1998.
It was left to Israeli Idan Tal to give Walter Smith's side a share of the spoils as he crashed in a left-footed drive into the corner of the net in the 78th minute.
Click below for an in-depth report on the game.
Everton 2 Middlesbrough 2
