Ayegbeni Yakubu grabbed a point for Everton with a second-half equaliser against his former club.
Middlesbrough had led from the eighth minute when Gary O'Neil scored after breaking down the right onto a Stewart Downing pass.
Everton battled away for parity and it eventually came after 65 minutes when Yakubu deflected a free-kick home off his back.
Everton pressed early on through Leon Osman and Phil Neville on the right, but were stunned by a Boro goal after just eight minutes.
Tuncay Sanli had seen one 20-yard shot go wide before an astute Stewart Downing pass exploited space down the right flank.
striker's feet
Joleon Lescott had been sucked into the middle, and there was Gary O'Neil to run into the box and fire low past Tim Howard.
Tuncay had another effort over the bar, again from a Downing pass, before Yakubu almost pulled Everton level.
He muscled his way past Emanuel Pogatetz on the edge of the box, but Ross Turnbull saved well at the striker's feet.
Lescott almost made amends when his swirling cross from the left hit the far post after 23 minutes. The ball dropped for Fellaini six yards out but his hooked effort was blocked almost on the line by Pogatetz.
Tuncay was proving a real handful for Everton's defence, and he almost created an opening for Afonso Alves with a clever pass, only for Joseph Yobo to snuff out the danger.
Phil Jagielka and Tim Cahill both had near-post headers that went close, before Yobo rose to meet a Neville cross, his header just clearing the bar.
fine move
Cahill then saw another header from Mikel Arteta's corner bounce wide of a post from close-range.
A minute later Boro almost caught Everton on the break when Alves and Tuncay raced away, the ball eventually finding Arca, but he hooked his shot over the bar.
Then Osman held off both Justin Hoyte and Wheater before drilling a low shot straight at Turnbull.
Everton had upped their tempo by now, and a fine move involving Arteta and Neville ended with a cross that saw Louis Saha send a fierce header just over.
Didier Digard was then booked for a trip on Arteta and when the midfielder fired over the free-kick, Yakubu claimed a 65th minute equaliser, the ball deflecting in off his back.
Boro responded with a Digard shot that Howard pushed onto a post, but neither side was able to find a winner.
