Chelsea had taken one point from their opening two matches but Spain forward Pedro, signed this week from Barcelona, opened the scoring and created a goal for Diego Costa before Cesar Azpilicueta added a third.
James Morrison atoned for an earlier penalty miss to score twice as West Brom looked to capitalise on the 54th minute dismissal of John Terry -- who was substituted for the first time ever under Jose Mourinho in last week's loss at Manchester City -- but Chelsea held on for their first win of the season.
City maintained their perfect start to the campaign against previously unbeaten Everton at Goodison Park to move top of the table on nine points ahead of Leicester City and Manchester United who have seven after three games.
City defender Aleksandar Kolarov opened the scoring on the hour before substitute Samir Nasri collected a deft pass from Yaya Toure to clip a sublime finish past goalkeeper Tim Howard in the 88th.
Southampton, yet to win this season, were held to a goalless draw at promoted Watford, who have now drawn all three matches since returning to the top flight this season.
(Reporting By Tom Hayward, editing by Jon Boyle and Ken Ferris)
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