Wolves looked to be heading for a much-needed victory when striker Kevin Doyle put them ahead with his third goal of the season, after 75 minutes.
Wolves goalkeeper Wayne Hennessey had earlier produced a string of fine saves to keep Wolves in the match, but with two minutes of normal time left the £10million Everton new boy struck with an equaliser.
Wolves ended the match with 10 men when substitute Stefan Maierhofer was sent off in injury time.
Everton successfully defended their right to field Marouane Fellaini following a row with the Belgian federation but opted to put him on the substitutes' bench.
The only change from the side that drew with Stoke last time out for the Toffees was the return to the heart of defence of Joseph Yobo as captain.
Wolves had striker Sylvan Ebanks-Blake making his first league start since the opening game of the season, when he suffered a hamstring injury against West Ham.
Ebanks-Blake added strength and running power up front and Wolves could easily have been ahead before half-time.
Greg Halford's long throw was a key part of their armoury and when he launched one into the box early on Christophe Berra's shot had to be charged down by Yobo.
Everton struggled to get going, although they went close when Louis Saha latched on to a long ball from Sylvain Distin and set up Tim Cahill for a rising shot on the run which flashed over the crossbar.
Wolves continued to cause Everton problems when they got the ball into the danger zone and Doyle produced a fine turn and shot from 15 yards to forced Everton goalkeeper Tim Howard into a fine save to his right.
Michael Kightly was booked for bringing down Leighton Baines but although Everton increased their tempo they did not do much to trouble Hennessey.
Twice just before the break Wolves could have scored, first when Halford touched a pass to David Edwards and the move ended with a shot from Ebanks-Blake that cannoned wide with Howard flat-footed.
Wolves went even closer a minute later when Doyle dummied Ronald Zubar's cross from the right and Ebanks-Blake rolled a shot inches wide.
Everton needed more punch up front and manager David Moyes sent on Ayegbeni Yakubu to partner Saha, taking off Tony Hibbert at the break and pushing John Heitinga to right-back.
They also needed the ball delivered more quickly and Baines responded within 60 seconds of the restart with an angled cross that Saha met with a downward header, saved well by Hennessey at the near post.
Hennessey then made a fine point-blank save when Bilyaletdinov found himself clear on the right of the box following a Baines crossfield ball, the Wales goalkeeper bravely getting his body in the way.
Wolves then took off Kightly, sending on Matthew Jarvis. But it was Hennessey who was again outstanding soon after, turning away a Saha drive at full stretch.
Ebanks-Blake forced Howard into a plunging save before Yakubu broke down the left and fired a shot across goal at the other end.
A minute later former Everton forward Segundo Castillo came on in place of Halford before Edwards was booked for pulling down Baines as the contest heated up.
Everton sent on Brazilian striker Jo for Saha, but it was Wolves who grabbed the lead after 75 minutes from the increasingly impressive Doyle.
He latched on to a long clearance from Hennessey straight down the middle, and ran on to guide his shot wide of Howard.
Austria international Maierhofer was booked after a tangle with Cahill and Everton grabbed an equaliser after 88 minutes when Jo crossed from the left and Bilyaletdinov arrived on the far post to drive home.
Maierhofer was shown a second yellow card for a foul on Howard in injury time and was sent off, with the American goalkeeper booked for retaliating.