The sides were level on 23 points before kick-off and on the periphery of the Barclays Premier League relegation zone but first-half debut goals from Blackpool loanee Tom Ince and Wales international Joe Ledley saw Palace on their way to a 3-1 victory.
A contentious Marouane Chamakh penalty then made sure of the points after West Brom's own debutant, Thievy Bifouma, struck early in the second half.
Palace have struggled for goals lately with only Jason Puncheon finding the net in the league since Boxing Day but they followed up their impressive FA Cup victory at West Brom last month with another success over the Baggies.
The Eagles have now taken 16 points from a possible 21 at Selhurst Park since Pulis replaced Ian Holloway in November as West Brom remain winless under Pepe Mel. The win enhances Pulis' hopes of continuing his record of having never been relegated and of becoming the first manager to keep the Eagles in the Premier League beyond a single campaign.
Kagisho Dikgacoi had an effort cleared off the line by West Brom's Youssouf Mulumbu, whose clearance hit Scott Dann but bounced high over the crossbar.
Yannick Bolasie was the next man to come close as he headed Jason Puncheon's cross straight at Ben Foster but the Eagles did not have to wait too long to break the deadlock.
Bolasie broke through and was brought down by Liam Ridgewell. Referee Chris Foy allowed play to continue and Ince beat Foster to the loose ball to score less than 15 minutes into his debut.
Craig Dawson smashed a speculative volley well over the top of Eagles goalkeeper Julian Speroni's bar as the visitors looked to level but it soon got worse for Mel's side.
This time Ince turned provider as his corner was met by Ledley who headed home unchallenged to double the Eagles' lead.
Bifouma was introduced alongside Scott Sinclair for the start of the second half and the striker, on loan from Espanyol, needed just two touches to add his name to the list of debutant goalscorers.
The 21-year-old played the ball out to Victor Anichebe before running onto the return and forcing it past Speroni at his near post to get the Baggies back into the game less than a minute into the second half.
With West Brom pushing further forward in search of an equaliser as the half progressed, the likes of Ince, Bolasie and Chamakh started to find more space to run into.
But, with those extra numbers in attack, Mel's side were also proving more of a threat in and around the Palace box as both James Morrison and Sinclair forced superb saves out of Speroni.
His opposite number Foster was then involved in the game's most controversial moment as he burst from his line and challenged Chamakh, who was clean through on goal.
The former England goalkeeper took the ball but Foy pointed to the spot, before deciding against showing a card to Foster, and Chamakh dusted himself off to convert the penalty and wrap up the win for Palace.
The home fans were given further cause to cheer when striker Glenn Murray returned from the knee injury which had kept him sidelined since the first leg of the Championship play-off semi-final against Brighton in May.
West Brom came close to narrowing the margin as Morrison, Anichebe and Saido Berahino all came close late on but it ended as a 10th defeat of the season for the Baggies, who will end the weekend in the bottom three.