Chelsea signed Pedro from Barcelona on Thursday and the Spain forward made an instant impact at The Hawthorns.
The 28-year-old opened his account for the champions with a deflected 20th-minute strike, but only after the returning Thibaut Courtois had saved James Morrison’s penalty six minutes earlier.
Jose Mourinho’s men made it 2-0 on the half-hour mark when Pedro set up Diego Costa for his first goal of the campaign, before Morrison redeemed himself by pulling one back.
Cesar Azpilicueta’s maiden Premier League goal then re-established Chelsea’s command of the match as they went in 3-1 to the good at half-time.
However, Chelsea captain Terry – who was substituted at half-time of last week’s chastening 3-0 loss at Manchester City – saw red early in the second period for hauling down Salomon Rondon.
West Brom, without Saido Berahino amid talk of an impending move to Tottenham, took advantage soon after through a superb Morrison header, but could not complete the comeback as 10-man Chelsea held on.
Costa dragged an early effort wide but Chelsea looked set to fall behind when Nemanja Matic tripped Callum McManaman just inside the area.
Morrison stepped up, but Courtois was equal to the midfielder’s low spot-kick and turned the ball over the bar with his legs.
And West Brom were punished six minutes later as Eden Hazard flicked the ball into Pedro, whose left-footed shot from the edge of the area took a deflection off Jonas Olsson and into Boaz Myhill’s bottom-left corner.
Chelsea then doubled their advantage with a superb counter-attack rounded off by Costa.
Willian fed the ball to Pedro and his shot across goal was turned in by international team-mate Costa from point-blank range.
A sloppy spell of Chelsea possession presented the hosts with a way back into the game as Rondon acrobatically turned James McClean’s deep cross into the path of Morrison to lash a shot past Courtois.
More good work from Pedro was wasted as Willian spurned a glaring chance for 3-1, but Chelsea did restore their two-goal advantage through Azpilicueta’s composed 42nd-minute finish after Costa had cushioned a ball over the top to the onrushing full-back.
Any hope of a comfortable second half for Chelsea evaporated with Terry’s dismissal, and Tony Pulis’ men capitalised five minutes later.
Morrison rose highest to head McManaman’s excellent cross from the left in off the crossbar and set up a frantic finish.
Costa and Rondon went close at either end before McManaman spurned the best chance to earn a share of the spoils as Chelsea held firm to collect a hard-earned three points.