The Irons also lost last time out despite taking a 2-0 lead versus Watford at The London Stadium. The Hornets equalised on the stroke of half-time in Stratford, before a James Collins own goal and an Etienne Capoue strike saw Walter Mazzari's take an unlikely three points.
Baggies winless since opening day
Pulis' men had their backs to the wall at The Vitality Stadium last Saturday and when it looked as though they had finally weathered the Cherry storm, Callum Wilson slotted home 11 minutes from time to snatch what would have been a hard-earned away point.
Of greater concern for the West Brom fans are their growing goal malaises. New signing Nacer Chadli was unable to make an impact on his Baggies debut and will be hoping to make himself instant Hawthorns hit this time round.
Pulis future continues to be shrouded in doubt with reports that the Welshman have been considering his position, after another disappointing transfer window.
Salomon Rondon and Gareth McAuley are the only names on the scoresheet so far this term, a statistic the hosts will be looking to remedy on Saturday.
Bilic beginning to feel the pinch
West Ham have not suffered such goal droughts, however their leaky defence is becoming a source of ire amongst the Irons' fans.
Boss Slaven Bilic has seen his side win just the once and lose on the three other occasions. The Hammers sit in 17th spot and whilst still early days, a second-successive Europa League Playoff elimination has turned the heat up on Bilic.
With Aaron Cresswell out with a long-term injury, Arthur Masuaka has been unable to fill the club's player of the year in 2014/15 and with Sam Byram on the opposite flank and lacking top-level experience, the defence have hit problems.
West Ham are however easing back both Dimitri Payet and Manuel Lanzini back into fold. With the Frenchman notching a double assist in his first game back, hopes are high that Bilic' side's early slump is merely temporary.
Irons' superior Premier League record
In the modern Premier League era, both sides have met 16 times. West Ham have the vastly superior record with double the six wins, to West Brom's three. There have been seven draws in the fixture's history, but just two goalless draws.
The last time the two met, the Hammers resoundingly swept aside Pulis' men. A brace from Mark Noble helped West Ham to a convincing win in the West Midlands.
West Brom still have an almost clean bill of health. Tony Pulis sole absentee is Chris Brunt, who has had his return from an ACL injury delayed until the end of October.
West Ham may have Andy Carroll back after a knee injury, however Diafra Sakho is still a few weeks away. Andre Ayew and as documented, Aaron Cresswell are out until late November with knee and thigh injuries respectively.