It certainly could have been a different story in the first period as Jay Rodriguez should have given them the lead in the tenth minute, but The Blues took over from there with a decent chance from Davide Zappacosta before Hazard opened the scoring in the 25th minute.
Once again West Brom wasted a golden opportunity through Salomón Rondón just before the hour mark, but again Chelsea turned it up another gear with Moses' effort before Hazard added a third in the 71st minute to round off an easy three points for the London outfit.
Wasting a golden chance
It had been quite the week or so for Conte's men with his tenure hanging by a thread after two consecutive defeats, Alan Pardew was dealt an early blow with the injury to star striker Daniel Sturridge but it seemed to buoy The Baggies as they should have added to Conte's misery with the opening goal ten minutes in.
To make it that much worse, it was handed on a plate to the visitors as Moses' weak header back to Thibaut Courtois fell straight into the feet of Rodriguez, the striker seemed to have all the time in the world but decided to go for the first-time effort which he skewed well wide of the mark.
Drawing first blood in some style
That scare seemed to kick Chelsea into life however and that showed in their increasing dominance, and after a decent opportunity, they managed to draw first blood.
The chance came in the 18th minute as César Azpilicueta's ball glanced past Oliver Giroud, but it did fall perfectly for Zappacosta at the back post but Ben Foster did well to get across and keep it out.
They eventually took the lead seven minutes as their patient build-up proved dividends, the move burst into life through Hazard who played the give-and-go with Giroud before the Belgian cleverly slotted home.
Another chance wasted
The fans inside Stamford Bridge will have felt a sense of Déjà vu at the beginning of the second period, as West Brom were handed another great opportunity to get themselves back in the clash.
A long ball from the West Brom defence worked well for Rondon as he managed to get the better of and outmuscle Andreas Christensen, he only had Courtois to beat but the Belgian somehow came out on top to deflect it behind.
Rounding off the win in some style
Once again Chelsea managed to waver the mini Albion storm and turned up the class, and two goals in eight minutes rounded off their resounding victory.
Moses doubled their lead in the 63rd minute as he started the move with a mazy run inside from the right, the Nigerian continued his run and was rewarded as Cesc Fàbregas' ball was deflected into his feet and he coolly slotted it under Foster.
Hazard started and finished the scoring and it was once again a great move from the Belgian, more patient build-up play came to the winger as he turned the defender on the edge of the area and smashed it in at the near post with Foster rooted to the ground.