Fabio Silva topped off a very good first half performance by Wolves when his attempt looped over Sam Johnstone.
But Mbaye Diagne's free header levelled the scoring early in the second half to rescue a point. The point doesn't do much to the Baggies' survival hopes as they face Arsenal, Liverpool, West Ham United and Leeds United in their final four games.
Neither side could find a winner in horrid conditions in West Bromwich and the game concluded in the 15th draw between the two sides.
Story of the match
After suffering a thumping 4-0 home defeat to Burnley last weekend, Nuno Espirito Santo made three changes to the side with Fabio Silva, Vitinha and Owen Otasowie all coming into the starting line-up.
After persisting with the tried and tested back five, Wolves returned to a 4-2-3-1 system- a formation that provides more chances but sees them leak more goals.
Romain Saiss partnered Conor Coady in defence with Leander Dendoncker and Ruben Neves pulling the strings from midfield. Adama Traore and Owen Otasowie were Wolves' wide players in between 21-year-old Vitinha.
The games first chance came on 11 minutes when West Brom's defensive corner problems continued. Vitinha picked out the head of the unmarked Saiss, but the Moroccan headed straight at Johnstone.
Wolves were better in every possible way than the Baggies and denied their rivals of any chance of catching Wolves on the counter as they dominated the possession- the Wanderers had well over half the possession in the first half.
They should have been 1-0 up just before the half-hour mark when Nelson Semedo robbed Semi Ajayi off the ball before being denied his first Wolves goal by a brilliant save by Johnstone.
Johnstone was called upon again when Vitinha was allowed all the freedom in the world before unleashing a swerving strike towards goal.
The Baggies were forced into an early switch when Matt Phillips replaced O'Shea after the former Exeter City defender suffered a minor injury.
Against the run of play, West Brom should have gone ahead when Ajeyi had his header blocked off the line by Saiss after Conor Gallagher's teasing cross found the head of the striker at the back post.
Wolves, deservedly, took the lead on the brink of half-time when Silva scored his second goal against the Baggies this season with a stroke of luck.
Otasowie, who looked sharp whenever the ball, cut in from the right before Vitinha's quick flick played Semedo through on goal. The right-back was unselfish and provided Silva with the chance to score.
Kyle Bartley got to the ball first but his attempted clearance rebounded off the teenager and looped over Johnstone to put Nuno's side into the lead.
Despite falling a goal behind so close to the interval, Albion came out in the second half more dangerous and with more purpose.
Conor Townsend fired his attempt right at Rui Patricio before the Portugeuse goalkeeper did superbly to deny Gallagher at the back post.
The latter of the two challenges clearly frustrated Nuno, with Gallagher being allowed far too much room in the Wolves area.
Allardyce's side levelled the scoring on the hour mark when Diagne headed in Townsend's cross after peeling off Saiss in the six-yard box.
The goal is the striker's third Premier League goal since his January arrival from Galatasary.
Wolves were forced into a late defensive change when Rayan Ait-Nouri was replaced by Max Kilman in what looked like a muscle injury.
First half most composed Wolves performance of the season
After being outclassed and easily beaten by Burnley last weekend, there were many fears amongst Wolves fans about suffering a fourth successive league defeat to their rivals.
But it wasn't the case at all. Wolves dominated possession, registered attempts on goal and minimised the threat from West Brom's dangermen.
The back four meant more numbers in midfield, which was one of the most telling points in their win. With Neves and Dendoncker adding experience, Vitinha and Otasowie provided the quick, diligent and trickery they have missed since Pedro Neto got injured.
Despite being denied on a couple of occasions by Johnstone, Wolves kept their nerve and patiently waited for the right moment to punish West Brom.
Owen Otasowie and Vitinha are ready to feature more
Calls for Vitinha to feature more often have been alive since he impressed in the U21 European Championships in the previous international break.
On loan from FC Porto, Vitinha has only one goal to his name since arriving in England but has shown glimpses of what he can do when presented the opportunity.
His low centre of gravity and flair was a vital clog in Silva's opener after he flicked the ball almost as easy as passing the ball five yards to break the Baggies defensive block.
Deployed on the right and as a number 10, Vitinha impressed in the pouring rain in the West Midlands and will fancy his chances of earning a permanent summer move to Molineux.
Otasowie, who stood out in the Wolves' under-23s victory over Norwich City last week, looked right at home in a Premier League clash.
The American midfielder first emerged onto the scene in the 2-1 victory over Chelsea earlier in the season but has since struggled for minutes in the first team.
However, after suffering from injuries and only having a small squad, Nuno put his trust in the 20-year-old and played him as a right midfielder. Not his natural position, but you wouldn't be able to notice.
His pace, strength, and ability on the ball all meant for a positive 70 minutes for Otasowie and is more than capable of future features.