Eden Hazard scored a brace for the Blues in the encounter.
It was Moses’ second league goal of the season in what was his 20th Premier League appearance for the West London club this term.
The former Wigan Athletic star was involved from start to finish in the game.
Chelsea also moved to the fourth position in the table with the win, one point behind Liverpool who sit in third position.
Chelsea went into the game low on confidence after winning three out of 10 matches in all competitions in 2018 and two back-to-back defeats against Bournemouth and Watford.
West Brom suffered a big setback early on when Daniel Sturridge sustained an injury after colliding with Cesar Azpilicueta and had to be replaced by Jay Rodriguez.
After a nervy start to the second half, Moses doubled Chelsea’s advantage in the 64th minute.
Cesc Fabregas’ pass was deflected into the path of the Nigerian and he camly slotted the ball beyond Forster.
Hazard got his second of the game eight minutes later to put the game totally beyond the visitors.
The Belgian cut inside on his left and blasted the ball past a wrong-footed Forster.