This is not Hazard's first mistake in this sense -- it's been a common theme of his period at Chelsea. For all of his brilliant attacking qualities, his mesmeric ball control and searing acceleration, he's staggeringly sloppy in a defensive sense. As long ago as 2013-14 it cost Chelsea in the Champions League semifinal, when Hazard twice switched off to allow Atletico Madrid defender Juanfran (who, coincidentally, holds Spain's right-back slot ahead of Bellerin) past him on the overlap for two goals.
It's reached the stage where Conte needs to consider creating a defensive shape to accommodate Hazard's sloppiness. Rather than defending with a back four and a line of five, perhaps Chelsea should simply defend with two banks of four, with Nemanja Matic shifting across to cover the left side of midfield. If Diego Costa dropped deeper, as he did so effectively during his Atletico Madrid days, Chelsea could create a 4-4-2 shape without the ball and 4-3-3 in possession. Carlo Ancelotti did something similar with Real Madrid because of Cristiano Ronaldo's similarly poor defensive qualities.
The shape wasn't helped, meanwhile, by the use of Cesc Fabregas in midfield. He played his way into the side with two goals in midweek at Leicester City, but here demonstrated precisely why Conte doesn't trust him in this system. Fabregas played too high up the pitch, creating a gap in Chelsea's defensive block that Arsenal were able to exploit. Playing both Hazard and Fabregas together in a side seeking to defend so deep was always going to cause problems.
Then came Arsenal's third goal, which featured Ozil spinning N'Golo Kante majestically, before playing a pass into the path of Sanchez, motoring into the box for the return ball and crashing a bouncing shot in off the far post. 3-0. This time, it was Chelsea's lack of defensive pace that was exposed, and Conte will be particularly disappointed at how easily Kante was beaten. The Frenchman's role in this side is to stay solidly in front of the defence, protecting the centre-backs from precisely that sort of counterattack.