After Dwight Gayle had given Rafa Benitez's men a surprise 12-minute lead, the Blues fought back with efforts from Álvaro Morata and a second from Hazard from the penalty spot, to give the hosts a comfortable win against an error-strewn Magpies defence.
The visitors opened the scoring after a bright from the Magpies and after clever work from Jacob Murphy on the right saw, the winger scampered inside the Blues' defence. Chelsea 'keeper Thibaut Courtois' effort to block the run, saw the ball squirm across to Dwight Gayle who was left with a simple finish to give Newcastle the lead.
In truth it the least Newcastle deserved after sluggish start from the hosts, but the the goal forced a response from Antonio Conte's men. After a barrage of pressure including a contentious penalty decision after Morata was felled by Karl Darlow and an Andreas Christensen header that crashed off the bar, Hazard levelled the scores in the 21st-minute.
Following a searching ball for the elusive Morata, the Spaniard's sliding effort to reach the ball was poorly dealt with and the ball rebounded out to Hazard, as the Belgian' shot bounced off the turf and over visiting stopper Darlow.
Morata gives hosts the lead
With the West Londoners buoyed, Morata then did give Chelsea the lead after further defensive lapses - this time from Matt Ritchie. Victor Moses pounced on the Scot's error and whipped a cross towards the goal, with Morata on hand to head home from barely a yard out.
Conte's men then took firm control for the remainder of the half with a long-range effort from Danny Drinkwater bending wide from goal, as the Blues lead 2-1 at half-time.
The visitors were keen to begin the second period as they begun the match and looked lively down the right flanks, but Chelsea quickly established superiority once more.
Hazard's deflected shot off Ciaran Clark ten minutes after the break went narrowly past the near post. Seconds later the Belgian flyer then had a penalty appeal waved away after tumbling in the box after pressure from the Magpies' defence.
Moses had a header straight at Darlow before Hazard again forced the new Newcastle number one into a low save. Lovely interplay between Drinkwater and Hazard, then saw the England midfielder chip a delightful bending ball in for the forward but was again denied by Darlow down low, after diving in to prevent an effort on goal.
Hazard adds second from the spot
The Blue tide finally saw the hosts add a third when Ritchie who had had not had the happiest of afternoons, tripped Moses after a lunge inside box. Hazard stepped up to impudently loft the ball over Darlow from the penalty spot.
Marcos Alonso came close to adding a fourth after his fierce shot was palmed away by the industrious Darlow with Hazard himself close to his hat-trick - before being substituted as Chelsea eased home to a comfortable 3-1 win at the Bridge.
Next up for the Blues is the visit of Atletico Madrid in the UEFA Champions League on Wednesday as Chelsea look to secure top spot in the Group standings.