Wilfried Zaha, who pre-match became the first Premier League player not to take the knee, won the spot-kick and Roy Hodgson saw his players keep a third clean sheet from their last four games to secure a vital victory.
It was a different story for the visitors who lacked a cutting edge and look certain to be in the Sky Bet Championship next season.
The Baggies were unchanged while the hosts recalled Zaha in place of Andros Townsend at Selhurst Park.
After Palace's top goalscorer marked his return from a hamstring injury with a cameo at Tottenham last weekend, he was back in the starting XI and it gave him the chance to stand at kick-off instead of taking the knee.
Zaha stated last month the pre-match gesture – brought in by the Premier League in June as an anti-racism message when football resumed – had lost its meaning and in a statement on Saturday insisted "it doesn't matter whether we kneel or stand, some of us still continue to receive abuse."
Once the Eagles attacker had stood at kick-off, while the 21 other players on the pitch took the knee, play got under way but chances were few and far between.
It was West Brom who enjoyed the better of the early exchanges and the impressive Okay Yokuslu should have done better in the 20th minute when he fired over from a promising position.
Sam Allardyce, who had a five-month spell in charge of Palace back in 2017, saw his old team make his current side pay the penalty in the 37th minute.
Central to the opener was Zaha, who saw a cross blocked by the arm of defender Darnell Furlong and following a lengthy VAR check, referee Simon Hooper pointed to the spot after using the pitchside monitor.
Milivojevic had a superb volley brilliantly denied by Baggies goalkeeper Sam Johnstone moments after the penalty incident and was able to get the better of him this time from 12 yards to open his account for the season.
While it was harsh on the visitors, it was almost 2-0 just two minutes into the second period.
Christian Benteke and Ebere Eze combined outside the area, but the former saw his rising effort excellently tipped over by Johnstone.
Palace were almost left to rue their profligacy when Conor Townsend picked out Matt Phillips in the 53rd minute and yet he blazed over on the volley after Patrick Van Aanholt had mistimed his jump at the back post.
The downpour showed no signs of slowing and it made life difficult, which neatly summed up West Brom's chances of survival with time running out.
While the rain did eventually stop, the Baggies were unable to find a leveller and fired another blank to suffer a 20th league defeat of the campaign.
It left Allardyce's men second from bottom and eight points from safety with nine fixtures left, but the picture is brighter for Palace who are up to 11th and on 37 points – a total which has been enough to avoid the drop in each of the last four seasons.