Hazard and Alvaro Morata gave the Blues an early two-goal advantage, and Marcos Alonso added to the lead before half-time. West Brom didn't have any answers for Chelsea, and Hazard doubled his tally after the break.
Here's a look at the teamsheet, via Simon Johnson of the London Evening Standard:
The Blues predictably started the match on the front foot but were given an early warning when Salomon Rondon found the back of the net from an offside position. The goal didn't stand, but the Chelsea defence gave the forward far too much space and had to be careful not to do so again.
Chances were rare, but the visitors took the lead with their first good look on goal. Hazard drew a fine save from Ben Foster after a brilliant run, and Morata pushed home the rebound.
Per Matt Law of the Telegraph, Hazard didn't make any friends with his celebration:
And he drew the ire of the home fans even more just minutes later, as he was booked for a horrendous tackle on Grzegorz Krychowiak. The Polish midfielder had sent Hazard to the turf earlier.
The former Lille man continued to play a leading role in the first half, doubling the advantage after 23 minutes. Morata sent him through on goal with a lovely flick, and Hazard rounded Foster before finishing.
Goal's Nizaar Kinsella loved what he saw from the duo:
West Brom had no answers, and Foster nearly made things worse when he decided to be adventurous near his own goal and almost gave the ball away to Morata, who was pressing the 'keeper. Luckily for Foster, the Spaniard couldn't put the ball in the net.
The Baggies were desperate to hold on until half-time, but even that didn't happen. A free-kick by Cesc Fabregas fell to Alonso, who calmly slotted a volley past Foster.
Per Law, the home fans turned on manager Tony Pulis:
Pulis introduced Claudio Yacob to start the second half, and West Brom got more of a hold in midfield but didn't create chances, though their solid spell of possession meant Chelsea couldn't trouble Foster anymore.
The Blues didn't have to work hard for looks, however, and with half an hour to play, Fabregas easily picked out Hazard, who fired in his second goal of the match.
More from Kinsella:
Morata also could have added a second but rushed his finish after great work by N'Golo Kante, while Gareth Barry fired a free-kick straight at Thibaut Courtois.
James McClean somehow failed to score from a great position, firing wide to keep Chelsea's clean sheet intact.
Yacob and Morata ran into late bookings, but the score remained unchanged as the defending champions cruised to the finish line.