New Baggies boss Tony Pulis was in attendance as Sam Allardyce's team slipped up in its pursuit of a Champions League spot
Pulis was appointed head coach at The Hawthorns earlier in the day - replacing Alan Irvine - and watched from the stands as Saido Berahino cancelled out Diafra Sakho's opener before halftime.
His strike ended a run of three straight Premier League defeats for the Midlands club while Sam Allardyce's West Ham failed to get back to winning ways after ending 2014 with back-to-back defeats to against Chelsea and Arsenal.
Despite West Brom starting well, Pulis watched on as his backline was carved open by a clever ball from Morgan Amalfitano, Aaron Cresswell subsequently crossing for Sakho to head home early on.
The good and bad sides to West Brom were then on show for Pulis as the visitors wasted several chances before the recalled Berahino eventually equalized three minutes from halftime.
Allardyce's side was much improved after the break but neither team was able to find a winner as West Ham remains sixth while West Brom stays a point clear of the drop zone in 17th.
West Ham's first foray forward came about from a slick passing move nine minutes in, which saw Cresswell stumble inside the area before he could connect with a shot on goal.
However, Cresswell was then instrumental in giving West Ham the lead when crossing for Sakho to head home his eighth Premier League goal 10 minutes in.
Former West Brom man Amalfitano played Cresswell in behind Andre Wisdom and the full back's delivery was met by Sakho, whose header found its way past Ben Foster off the far post.
As in the Boxing Day defeat to Manchester City, West Brom continued to waste chances as Stephane Sessegnon blazed wide when afforded time and space in the area.
Allardyce had brought Carl Jenkinson and James Collins into his defense and they were tested further when Chris Brunt evaded Collins - only to divert Sessegnon's pass wide before Berahino finally leveled shortly before the break.
Sessegnon - who shook off a knock to keep his place in caretaker Rob Kelly's starting XI - was again influential, bursting forward before squaring for the striker to sidefoot home.
Berahino was denied a second early in the second half by a sprawling Adrian as Kelly's men continued to impress before the home side eventually managed to regain a foothold in the game.
Cresswell's free kick struck Foster's left-hand post while Downing's cross from the right led to a goalmouth scramble, but the hosts failed to regain the lead as the spoils were shared in east London.