At a windswept Hawthorns that at times was under torrential rain, Wolves opened the scoring in first-half stoppage time when Kyle Bartley’s clearance hit Fabio Silva before looping over goalkeeper Sam Johnstone and into the net.
Sam Allardyce’s side were poor in the opening 45 minutes with the team possibly suffering a hangover after conceding so late to draw with Villa last time out - a result that severely damaged their hopes of pulling off a great escape.
But they improved after the interval and pulled level when Mbaye Diagne headed in a cross from Conor Townsend.
Both teams then pushed forward to find the winner fans craved.
But as the weather got worse, so did the football on show with the game petering out into a draw.
The result means the Baggies now sit 10 points from safety in the Premier League with just four games remaining.
In his time as Albion boss, Allardyce has shown a tendency to switch to a 3-5-2 formation when coming up against a team that likes to play with a back three.
And he did that here with Dara O’Shea coming into the side at centre-back where he partnered Kyle Bartley and Semi Ajayi.
The tactical change meant Matheus Pereira shifted from the right-wing to join Diagne up front.
In midfield, Okay Yokuslu operated in the holding role with Conor Gallagher and Ainsley Maitland-Niles either side. Darnell Furlong and Conor Townsend were deployed as wing-backs.
Albion’s plan to match Wolves man-for-man went out of the window before-kick off, though, with Nuno springing a number of surprises with his starting XI.
The Portuguese boss hinted in his pre-match press conference that Wolves had 'many injury problems heading into the game - and his team selection was unusual.
Opting for a 4-2-3-1 formation, Silva got the nod as the lone centre-forward ahead of Willian Jose.
In what was a very young squad, Adama Traore started on the left wing with 21-year-old Vitinha in the number 10 role and 20-year-old Owen Otasowi on the right.
There were also four teenagers on the bench in Ki-Jana Hoever, Theo Corbeanu, Luke Cundle and Christian Marques.
Willy Boly was absent from the matchday squad - with Nuno revealing the defender missed out due to suffering long-term effects from Covid-19.
Wolves entered the game needing to show a reaction from their dismal defeat to Burnley last time out, while Nuno’s side were also intent on revenge having lost the reverse Black Country derby in January.
And it was the visitors who started the brighter of the two teams with Neves driving at goal before firing wide in the first few minutes.
Romain Saiss then rose highest to meet a corner but his powerful header was straight at Sam Johnstone.
Albion responded with Furlong dragging a shot wide from the edge of the box following some nice link-up play.
But as the clock ticked towards the 20 minute mark, it was Wolves who were doing all the prodding and probing with Rayan Ait-Nouri dancing past three or four challenges to get into the box before finally being tackled.
With the rain continuing to lash down on The Hawthorns turf, the overall quality of the match continued to be poor with both teams struggling to find any real rhythm.
But as the half-hour approached, Wolves went up a gear and twice came close to opening the scoring.
First Ajayi intercepted a through-ball intended for Silva. But while he read that pass, the Nigerian international then dallied instead of making a clearance.
And that allowed Semedo to nip in and win the ball before carrying it past Bartley to leave himself with only Johnstone to beat.
Having done the hard work, the former Barcelona man really should have made the net ripple.
But his powerful strike was too close to Johnstone who did well to beat the ball away.
Wolves threatened again just moments later with Vitinha hitting a swirling strike from distance which Albion’s keeper again had to punch away.
And with his side now being constantly pegged back, an unhappy Allardyce decided to make a first-half change with Matt Phillips coming on and O’Shea the unfortunate man to make way.
That allowed Albion to switch to a 4-3-3 system with Phillips on the left flank and Pereira on the right.
And the change almost proved a masterstroke with the Baggies inches away from taking the lead just moments later.
After Gallagher whipped in a smart cross, Diagne did well to meet the ball at the back post and plant a header across goal and past Rui Patricio.
But taking up a shrewd position just in front of the goal line, Saiss managed to stick out a boot and deflect the ball to safety.
Albion immediately looked more settled in their system. But it was Wolves who, overall, had been the better side.
And they managed to get their noses in front in first-half stoppage-time.
First, Otasowie did well to burst past Townsend before finding Vitinha.
And he produced a wonderful flicked pass with the back of his heel to move the ball onto Semedo who then looked to lay it off to Silva.
Bartley got their first and looked set to smash the ball clear. But his clearance only succeeded in hitting the shin of Silva with the Portuguese forward then getting a huge slice of luck when the ball looped up over Johnstone and into the net.
It was Wolves who started the second-half on the front foot with Silva meeting a cross from Traore only to see his header comfortably claimed by Johnstone.
Albion responded and created two glorious chances to pull level in the space of 60 seconds.
First Pereira rode a number of challenges to find an unmarked Townsend around eight yards out.
The full-back only had the keeper to beat. But while he struck a powerful effort towards goal it was too close to Patricio who beat the ball away.
Then just moments later, Phillips rolled the ball right across the face of goal - with Gallagher set to simply side-foot it home.
But his strike lacked conviction and was also the perfect height for Patricio who flung himself across goal to push the ball away.
Wolves almost doubled their lead on the hour with Silva driving at goal before arrowing a drive towards the bottom corner which Johnstone did well to push away.
And after surviving that scare, Albion went up the other end and hauled themselves level in the 62nd minute.
It was Townsend who created it with the full-back whipping in a wonderfully inviting cross.
And an unmarked Diagne then nodded the ball home after completely escaping the attention of Saiss who lost the striker far too easily.
Nuno made his first change with a little under 20 minutes remaining with Otasowie replaced by Podence. The Baggies then introduced Callum Robinson for Maitland-Niles.
In the closing stages, The Hawthorns was being battered by wind and torrential rain.
With puddles of standing water appearing all over the pitch, it had got to the stage - with five minutes to go - that the surface had become hazardous for the players.
And that meant - while both teams tried to push for a winner - the game ultimately petered out into a draw with the surface preventing both sides from playing with any rhythm.
Albion (3-5-2): Johnstone, Ajayi, Bartley, O’Shea (Phillips 33), Furlong, Yokuslu, Gallagher, Maitland-Niles (Robinson 78), Townsend, Pereira, Diagne.
Subs not used: Button, Peltier, Livermore, Sawyers, Diangana, Grant, Robson-Kanu.
Wolves (4-2-3-1): Patricio, Semdo, Coady, Saiss, Ait-Nouri (kilman 82), Vitinha (Gibbs-White 80), Dendoncker, Neves, Traore, Silva, Otasowie (Podence 71).
Subs not used: Ruddy, Hoever, Cundle, Corbeanu,Marques, Jose.