Slaven Bilic's Hammers were unable to add to their early lead which came courtesy of a sublime bending free-kick from Mauro Zarate in the 17th minute.
Rickie Lambert's introduction at half-time inspired the Baggies to find an equaliser five minutes into the second half when the veteran striker's fierce effort from inside the area cannoned past Adrian with help from a wicked deflection off Winston Reid.
The result left West Ham in eighth position as Tony Pulis' Albion remained 13th after accruing their 18th point of the season.
- Are the bubbles at West Ham beginning to burst? How can Bilic get them back to winning ways?
- Baggies appear to be in no man's land where they are clear of the bottom three but not really pushing for a mid-table finish. Does Pulis need some winter reinforcements?
West Ham travel to Manchester United on Saturday in search of a first win in five outings as Albion prepare to host Tottenham at The Hawthorns.
1 more point but a shame not to get the 3 points after a great first half!Thank for your support as always⚒ #ADR13Npic.twitter.com/0r7sn8F76n
— Adrián San Miguel (@AdriSanMiguel) November 29, 2015
Thanks everyone for all your messages! It was so special to be back at Boleyn Ground and feel all your support! #COYI
— Pedro Mba Obiang (@Obiang14) November 30, 2015
.@salorondon23: "It's an important point for us, but we could have taken all three" https://t.co/d4uatTRXD7#WBApic.twitter.com/HIK1SScYCp
— West Bromwich Albion (@WBAFCofficial) November 30, 2015
West Ham boss Bilic admits his side should have put Albion to the sword:
"It's a fair result over 90 minutes, they deserved something from the second half - but in the first half we should have been more than 1-0 up.
"At half-time we were pleased with the way we had played. But by four o'clock I was not pleased with the result."
West Brom's Pulis on the influence of Lambert:
"He's a great professional. He has not played as much as he would have liked but his attitude is fantastic. The lads want to play and that's something you have to deal with.
"Rickie is a throwback to the times when footballers cared about football, and he cares. He has been a terrific signing for this football club."