Goals from Pedro, Diego Costa and Cesar Azpilicueta put Chelsea in command at The Hawthorns after Thibaut Courtois saved a penalty from James Morrison, who later scored.
Keeper Courtois, back from suspension, kept out Morrison’s 14th-minute spot-kick with his legs after Nemanja Matic had fouled Callum McManaman.
Six minutes later, Pedro marked his Blues debut with a goal.
The Spain international, signed from Barcelona this week, exchanged passes with Eden Hazard before seeing his shot take a deflection of West Brom defender Jonas Olsson and spin into the corner of the net.
And Pedro was involved in the second goal, collecting Willian’s ball down the right and then firing across goal for Costa to add the finishing touch.
Chelsea appeared to be cruising but Morrison then atoned for his earlier miss by reducing the deficit.
Once again Branislav Ivanovic, who has been poor so far this season, was at fault.
Chris Brunt sent in a deep cross from the left which Salomon Rondon kept in play by acrobatically volleying the ball back from the byeline, and Morrison belted home.
But Chelsea remained a threat and Willian missed a good chance to make it 3-1 before Azpilicueta netted a couple of minutes before the break.
Cesc Fabregas chipped forward and Costa held off Gareth MacAuley to chest the ball down to Azpilicueta, whose first-time shot flew into the bottom left-hand corner – his first Premier League goal.
Chelsea: Courtois; Ivanovic, Zouma, Terry, Azpilicueta; Matic, Fabregas; Pedro, Willian, Hazard; Diego Costa.
Subs: Begovic, Cahill, Mikel, Loftus-Cheek, Traore, Remy, Falcao.