Tim Cahill's strike just before half-time had looked set to deliver the points for David Moyes's side until Ebanks-Blake converted Kevin Doyle's cross as Wolves mounted a clinical counter-attack with quarter of an hour left.
Doyle returned for Wolves in place of the injured Steven Fletcher.
Leighton Baines then went close from another free-kick, awarded after Karl Henry fouled Steven Pienaar, and Dutch defender John Heitinga drew a fine save from Marcus Hahnemann with a drive from 25 yards out.
Pienaar fired an effort narrowly over before Everton finally made the breakthrough, two minutes before half-time, following a foul on Arteta on the edge of the area.
The Spaniard fired the resulting free-kick into the wall and Cahill was first to react, gathering the loose ball before smashing a left-foot shot high into the net.
Everton continued to dominate after the break with Jermaine Beckford, who slipped while shooting from an inviting position inside the box, and Bilyaletdinov, who scuffed his chance from a Cahill knockdown, both profligate.
Wolves had done little to suggest they might take something from the match but they produced an equaliser from nothing after substitute Adlene Guedioura won the ball in midfield and set Doyle clear down the right.
The home defence was badly exposed and the Irish forward's low cross enabled Ebanks-Blake to sweep home from close range.
Cahill and substitute Saha both went close in the closing stages but Everton were forced to settle for a frustrating draw.
Source: AFP Global Edition