Alan Pardew's outfit went ahead in the 30th minute when a long range James McClean effort deflected off Angelo Ogbonna and looped over Hammers goalkeeper Adrian.
As well as the McClean goal, Reid - playing on the right hand side of West Ham's back three - was also shaken off by WBA striker Salomón Rondón, who lobbed a shot onto the roof of the net.
Minutes later, Marko Arnautović had a clear cut chance to give the lead for West Ham but Foster continued his virtuoso performance as his ideal timing stopped the front man.
West Bromwich Albion have complained to the Premier League, urging them to reschedule Tuesday's clash at West Ham United because of the vast difference in recovery periods for the two teams, British media reported. Then just before the hour, Carroll glanced Aaron Cresswell's centre beyond Foster, finally restoring parity much to the relief of the previously agitated home crowd.
Simon Stone, a BBC online sports writer, posted a tweet on his official account prior to last night's match in which he backed Moyes to ring the changes this transfer window.
Video footage has emerged which shows the West Brom midfielder involved in a confrontation as he was being substituted in the 64th minute.
West Brom kicked off 2018 with a game against fellow strugglers West Ham at the London Stadium.
That was just two short months ago, yet the Winston Reid who played against WBA, now looks down on confidence.
It was the Irish midfielder's first goal of the season, and in fact the first he had scored since a 4-2 win over the same opposition in September 2016.
"We lost a goal in the last minute at Bournemouth which should have counted". He said: "I didn't know about it, but I've been told something happened".
"For the second one, I think "Manu" should have passed to me earlier", he laughed.
It was a characteristic under Bilic, but seems to have fallen away slightly under Moyes, however slow starts to matches can be fatal and we were lucky to get the three points we needed from this game.
I could not deal with the loss and the circumstances of it, as well as the pressures of everyday life and trying to keep my team in the Premier League.
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