Chelsea were unchanged from their win over Manchester United before the international break, but West Brom recalled Salomon Rondon and Matt Phillips as the Baggies looked to overcome a difficult run of form.
West Brom thought that they had taken the lead in the fifth minute when Rondon headed home from close range, but the centre-forward was flagged offside as the home celebrations were cut short.
Chelsea's first chance of the match arrived in the 14th minute when Tiemoue Bakayoko broke into the home side's penalty box, but the Frenchman's effort was deflected just wide of the post by diving defender Gareth McAuley.
The Blues did take the lead three minutes later, however, when Morata converted from close range after West Brom goalkeeper Ben Foster could only palm an Hazard strike into his own box.
Alonso had a decent chance to double Chelsea's lead in the 20th minute after meeting a loose ball on the edge of the box, but the wing-back's effort was always moving wide of the post.
The visitors were purring though and scored their second of the afternoon in the 23rd minute when Hazard raced onto a flick from Morata before finding the back of the net with a calm finish.
Foster just about got away with a heavy touch inside his own box in the 30th minute as Chelsea continued to threaten, and the home side's supporters were airing their frustrations as the first period approached its latter stages.
It went from bad to worse for the Baggies in the 38th minute when Alonso converted a Cesc Fabregas cross at the far post as the points were all but sealed before the half-time interval.
Jay Rodriguez sent one wide of the Chelsea post early in the second period as the home side looked to give their supporters something to cheer.
The visitors then came close to a fourth when Hazard darted into the penalty area before looking to pick out the bottom corner, but Foster was on hand to make a fine save.
Fabregas and Rondon were both booked trying to win penalties in the opening 10 minutes of the second half, while Foster had to be alert once again to keep out an effort from Morata.
Chelsea had their fourth in the 62nd minute, however, when Hazard collected a chipped pass from Fabregas before settling and finishing into the back of the net.
Morata whistled one over the crossbar 20 minutes from time as the visitors looked for more goals, but Hazard was given a rest as Pedro entered the field.
Gareth Barry curled a free kick into the arms of Chelsea goalkeeper Thibaut Courtois in the 75th minute, before James McClean sent one just wide of the post after breaking into the away side's box 10 minutes later.
McClean at least brought some excitement to the home side's supporters in the latter stages, but a sixth league defeat of the campaign has left the Baggies just one point outside of the relegation zone.