Saido Berahino's first-half strike proved the difference at The Hawthorns as the home side moved five points clear of the drop zone.
West Ham, however, have now lost their last four league games in a row.
Here, Sports Mole dissects the 90 minutes of action between the two Premier League rivals.
On target: 6
On target: 4
Was the result fair?
Although both sides had golden opportunities throughout the 90 minutes this afternoon, there is no question that West Brom deserved to secure all the points. There was understandably some nerves in the latter stages due to recent dropped points at home in the latter stages of matches, but Pepe Mel's side held on to secure a vital win. The visitors had their moments in what was an end-to-end afternoon of football, but did not offer enough in the final third to deserve something from the contest.
West Brom's performance
It was far from the Baggies' best performance of the season, but it was the result that mattered most this afternoon. Defeat would have left them teetering extremely close to the relegation zone, but they now sit five points ahead of 18th-placed Fulham, who have also played one game more. Mel decided to start with Berahino as the lone forward and it paid dividends as the England Under-21 forward opened the scoring. It should have been more comfortable in the second period, but the goalscorer and the likes of Stephane Sessegnon were guilty of missed opportunities. That said, it was an impressive rear-guard performance from the home side, with Jonas Olsson and Craig Dawson both dealing with the threat of Andy Carroll.
West Ham's performance
Once more, West Ham supporters travelled in their numbers this afternoon, but were left underwhelmed by another flat performance from their side. With the Hammers all but safe from relegation, it had been said that the majority of their players are already on their holidays. Well, it is difficult to argue with that notion. Granted, they had their opportunities this afternoon - with Carroll looking the most likely - but it was too predictable from the Hammers for long spells. Stewart Downing and Matt Jarvis both enjoyed positive first periods, but both wingers departed in the second half as the Hammers became short of ideas. With the long ball to Carroll not working, there was not too much in the way of a Plan B. A number of their influential players simply failed to turn up, which resulted in a fourth successive league defeat.
Sports Mole's man of the match
Jonas Olsson: If there is one centre-back in the league who relishes the physical side of defending, then it is Olsson. The 31-year-old came head-to-head with Carroll this afternoon and made it a largely frustrating afternoon for the England striker. The Swede was not only aerially dominant, but was also prepared to put his foot on the ball in the latter stages when those around him started to panic. It was a real show of leadership from the defender at The Hawthorns.
Berahino's first-half strike secured all the points for West Brom this afternoon, but the young forward was guilty of missing a golden opportunity in the second period. Bright work from Sessegnon led to Berahino having a free shot on goal from close range, but he fired his effort straight at West Ham goalkeeper Adrian. In the end it did not cost his side, but it really should have been more comfortable for the Baggies.
Incredibly, referee Mike Dean did not issue a single yellow card until the second minute of stoppage time at the end of the match when West Ham defender James Collins had his name taken. It was a composed performance from the English official, who was prepared to let the play flow in the correct areas rather than whistle for every slight challenge. The fact that the match was such an entertaining affair is partly down to Dean's solid performance in the middle.
West Brom: West Brom travel to top-four hopefuls Arsenal next Sunday.
West Ham: The Hammers will attempt to return to winning ways when they welcome London rivals Tottenham next Saturday.