Wolves had to battle all the way to take a point from in form Everton at Molineux. But Mick McCarthy's men made it four games unbeaten as they edged a little closer to Premier League safety.
The manager had named an unchanged side after the mid-week victory at West Ham and they kicked-off attacking the South Bank end. After two minutes Matt Jarvis was wide as he tried to deflect the ball in at the near post following a cross from Kevin Foley.
But it took a reflex save from Marcus Hahnemann to prevent the Merseysiders from taking a sixth minute lead. Steven Pienaar crossed from the right and Leon Osman looked odds on to score as he sidefooted the ball goalwards only for Hahnemann to throw himself to his right and palm the ball away.
Osman figured again as he fired wide after a Phil Neville long throw had fallen to him, and then Hahnemann saved a low effort from Louis Saha.
Everton were looking strong and another shot from Osman was taken by Hahnemann after the ball had taken a deflection off Michael Mancienne.
Dave Jones was crowded out as he tried to work a shooting position for himself just inside the Everton box and then a smart piece of work from Ronald Zubar saw the visiting defence opened up.
The defender left Osman in his wake and sprinted into the right of the Everton area. He lashed the cross into the heart of the goalmouth where it hit Phil Jagielka and flew behind. Jarvis took the flag-kick but Toffees keeper Tim Howard punched clear.
A tremendous shot from Saha was inches away from giving the visitors the lead in the 38th minute. He chested down a deep cross and then took a touch before smashing a shot against the angle from the edge of the box.
The crowd reacted with anger as the referee waved play on after John Heitinga had clearly fouled Jarvis.
There was a chance for Tim Cahill two minutes before the break after Jagielka lobbed the ball into the Wolves box. It fell to Cahill but he blazed a shot high over Hahnemann's bar.
Then it was Wolves' turn to go close. A Jarvis corner was headed back by Zubar to Jody Craddock who drove the ball over the bar from near the penalty spot.
In stoppage time Slyvain Distin fouled Kevin Doyle just outside the Everton 18-yard line but Jones's free-kick went straight to Howard.
Half-Time: Wolves 0 Everton 0
Inside two minutes of the resumption, Leighton Baines fouled Zubar to the right-hand corner of the Everton area. Jones took the free-kick but then found himself in the book for taking it before the referee had whistled. When it was retaken Jarvis decided to have a pot but Howard punched the ball clear.
A well timed challenge from Craddock was enough to put Saha off as he ran in onto Osman's centre - the French striker's header going over the bar.
Christophe Berra helped on a throw from Foley but when the ball dropped to Jarvis he hooked it high over the bar.
A Baines free-kick deflected wide off the defensive wall and when Baines took the resultant corner, Cahill headed wide of the mark.
Foley was penalised for what looked a perfectly good tackle on Pienaar but justice was done when Baines's free-kick went over everyone and out on the far side for a goal-kick.
After Pienaar was booked for a late challenge on Karl Henry, George Elokobi came to the rescue diverting a header from Saha that looked bound to present Cahill with an easy chance right in front of goal.
With 20 minutes remaining Adlene Guedioura replaced Mancienne before Foley curled the ball over the angle after Jones had touched a Jarvis cross into his path.
In the 74th minute Zubar almost repeated his heroics of Upton Park when he played a one two with Doyle on the right and raced into the area before lashing an angled shot narrowly over the bar.
Pienaar twice had the opportunity of breaking the deadlock in a two minute spell. His first shot took a deflection and flew wide and then he scuffed his second effort straight into the hands of Hahnemann.
Guedioura was high and wide with a spectacular overhead kick after a centre from Foley then, when Jarvis, Foley and Elokobi combined there was a tremendous scramble in the Everton goalmouth before Doyle hit a shot over the bar.
Cahill set up a chance for substitute Dan Gosling but Hahnemann spotted the danger and cut the ball out. The two collided and Gosling was only able to continue after lengthy treatment and even then he spent stoppage time limping heavily.
Deep into the added time, Craddock cleared an overhead kick from Cahill that was just about to cross the line.
Wolves: Hahnemann, Zubar, Elokobi, Mancienne (Guedioura 70), Craddock, Berra, Foley, Henry (capt), Doyle (Iwelumo 90), Jones, Jarvis (Ward 90).
Unused subs: Hennessey, Ebanks-Blake, Keogh, Milijaš.
Booking: Jones (47 - taking free-kick before whistle).
Everton: Howard, Baines. Heitinga, Jagielka, Saha (Yakubu 75), Distin, Cahill, Neville (capt), Pienaar, Osman (Gosling 83), Rodwell (Bilyaletdinov88).
Unused subs: Nash, Hibbert, Yobo, Senderos.
Booking: Pienaar (65 - foul).
Referee: M. Jones.
Wolves Academy Under 18s 0 Newcastle United 2