The Baggies produced a 3-0 result over the ten-man Blues at The Hawthorns on Monday night to end Jose Mourinho's side's 16-match undefeated streak.
Saido Berahino opened the scoring inside 10 minutes with his first goal in 10 matches when firing an arcing effort home from 25 yards.
That preceded a mindless red card to Chelsea midfielder Cesc Fabregas who kicked the ball against Chris Brunt's head as referee Mike Jones attended a fracas between Diego Costa and Gareth McAuley. It was the Spaniard's first send-off since 2006.
That helped open the game up, however, and Albion capitalised early in the second half when John Terry brought down Berahino in the area allowing the 21-year old to step up and beat Thibaut Courtois from the spot.
On the hour-mark, West Brom went further ahead when Brunt was given permission to advance into the area before powering beyond Courtois as Tony Pulis' side inflicted a third league defeat on Mourinho's men.
The victory saw Albion remain 13th on the table, taking their season tally to 44 points, ahead of next weekend's season closer at Arsenal.
2014/15 Barclays Premier League