The Belgian forward, purchased from Lille for a fee of £32 million this summer, had already created five goals in just two matches for Chelsea prior to Saturday evening's game, which took place amid a deluge of rain in West London.
And when Fernando Torres was brought to ground by Vurnon Anita after 22 minutes, responsibility for the penalty was handed to Hazard with Frank Lampard sitting on the bench and he struck the ball home with all the confidence of a man who has settled in immediately to Premier League football.
When Chelsea extended their lead in first-half injury time, it was inevitably Hazard who rolled the ball backwards impudently for Torres to toe-poke a brilliant shot into the top corner, his creative instincts continuing to help deliver a new brand of football from a side who relied on oppressively negative tactics to win the Champions League last season.
Chelsea were forced to do without captain John Terry due to a neck injury while Lampard, in a nod to his advancing years, was rested from the starting XI. Newcastle meanwhile made nine changes from their European fixture in midweek, with Anita replacing the injured Cheick Tiote for his full Premier League debut following a transfer from Ajax.
While Chelsea's new signings Cesar Azpilicueta and Victor Moses were presented to the Stamford Bridge crowd prior to kick-off - their acquisitions on Friday taking the club's summer spending past the £80 million mark - it was the most lucrative of the new arrivals whom all eyes were focused on.
Having created five of Chelsea's six goals in their opening two games of the season, Hazard has already developed quite the reputation in the Premier League and stationed out on the right against Newcastle he looked intent on wreaking yet more havoc.
After 14 minutes the Belgium international drifted inside, collected a short pass from John Obi Mikel and had a shot from 20 yards that lacked the precision or pace to trouble Tim Krul in the Newcastle goal. Team-mate Ryan Bertrand had a better chance soon after but also hit the ball too close to the Dutchman.
Chelsea posed only an intermittent threat but on 22 minutes Torres sprung to life as he surged into the box and drew a clumsy challenge from Anita. Phil Dowd pointed towards the penalty spot and Hazard continued his wonderful start to the season with the 10th conversion in 10 penalty attempts during his professional career, slotting the ball out of the reach of Krul.
Branislav Ivanovic - another one of the stars of Chelsea's early campaign with two goals to his name - threatened again when connecting with an Ashley Cole cross with a firm header, while Hazard then combined with Juan Mata before the Spaniard tried to cross for Torres when a shot would have been the superior option.
Torres was a more sprightly presence following his key intervention for the penalty, and the Euro 2012 Golden Boot winner thought he had Fabricio Coloccini in trouble after being brought to ground by the defender as he skipped away from him. However, Phil Dowd misread the situation and angered Torres by booking him for diving.
With Newcastle restricted to a half-chance from Papiss Cisse that saw the striker turn quickly and test Petr Cech with a firm shot, Chelsea extended their lead deep into first half injury time. Torres slipped the ball into Hazard, who returned the favour with a lovely flick into the path of the Spaniard. Spotting a gap in the top corner , Torres toe-poked a lovely shot out of the reach of Krul for 2-0.
Newcastle were a renewed force after the break and placed Chelsea under considerable pressure with a number of shots from range. Demba Ba then drove into the box following a mistake from Mikel to force Cech into a smart save from a tight angle.
However, Chelsea always looked threatening on the break and almost got in behind on 61 minutes when Torres muscled Anita off the ball in the box. Displaying the fresh flood of confidence flowing through his veins, the Spaniard even attempted a 'Rabona' cross but failed to pick out Mata when placing one leg behind the other and punting the ball into the middle.
Newcastle carved out perhaps their finest chance of the game after 68 minutes when substitute Ryan Taylor delivered a teasing, deep cross to the back post. However, Cisse - scorer of two otherworldly goals at Stamford Bridge last season - could not keep his header on target despite being left free in the box.
By contrast, Hazard was a constant menace and with 10 minutes remaining he almost picked out Ramires for a third goal after thundering into the box. The ball fell to Bertrand, who saw Krul get an outstretched finger to his shot and tip the ball round the post.
Newcastle could have ensured a tense conclusion when a cross from Sylvain Marveaux was headed back to Ba. Though he missed the ball at the first attempt, Ba's second effort was low and hard but Cech pulled off a fantastic save to protect Chelsea's 2-0 lead.
Hazard and Torres had done their job: Chelsea's stylish start to the season continued.