Hazard opened the scoring from the spot in the 22nd minute before laying on the second goal for Torres in first-half stoppage time.
Chelsea were without injured skipper John Terry and left vice-captain Frank Lampard on the bench, but still had enough quality and experience to dominate the opening 45 minutes before an improved Newcastle performance in the second half.
The victory saw the Blues maintain their perfect start to the new season and return to the top of the fledgling league table.
The opening 15 minutes were uneventful, with John Obi Mikel firing high and wide and Hazard shooting straight at Newcastle goalkeeper Tim Krul.
But the home side created the first real chance three minutes later.
Torres controlled a cross-field pass from Raul Meireles before rolling a ball just inside the box to Ryan Bertrand, whose effort was not strong enough to test Krul.
The European champions were ahead soon after, though, when Vurnon Anita - making his first Premier League start for Newcastle - brought down Torres just inside the area.
With regular penalty-taker Lampard on the bench, Hazard - who earned spot-kicks for his side in each of their first two games this season - stepped up and directed a low penalty past Krul.
Branislav Ivanovic nearly doubled Chelsea's lead just after the half-hour mark when he out-jumped Davide Santon to meet Ashley Cole's deep cross but his header was too close to Krul, who managed to keep the Serbia captain's effort out.
Hazard could have grabbed his second of the game five minutes later but he blazed over from the edge of the area as the hosts started to dominate possession.
Torres was then showed a yellow card by referee Phil Dowd for diving after knocking the ball around Fabricio Coloccini with the whole of the Chelsea bench up in arms as it appeared the Newcastle captain caught Torres with his trailing leg.
The visitors went close to equalising a minute before half-time when full-back Danny Simpson challenged David Luiz as he tried to carry the ball out of the box.
The loose ball broke for Papiss Cisse, but his snap-shot - although hit with venom - was straight at Petr Cech, who held the ball well.
There was still time before the interval for Chelsea to double their lead as the impressive Hazard back-heeled the ball perfectly into the path of Torres, who finished coolly into the top corner.
Newcastle came out in the second half looking for an early goal to get themselves back into the game.
First Hatem Ben Arfa wriggled free before shooting wide before Jonas Gutierrez followed suit moments later.
Demba Ba then forced Cech into a smart save with his legs after breaking free inside the Chelsea penalty area.
With the visitors starting to get a foothold in the game, Roberto Di Matteo introduced Ramires off the bench in place of Juan Mata to add more guile to the Chelsea midfield.
But it was Newcastle substitute Ryan Taylor who almost orchestrated the third goal of the game.
His deep free-kick was met by the head of Cisse but the Senegal striker could not keep his effort down and it comfortably cleared Cech's crossbar.
With Newcastle pushing forward Chelsea were able to launch several counter-attacks and Bertrand almost scored a third with 10 minutes to go but his drilled effort was deflected past Krul's far post for a corner.
Magpies boss Alan Pardew introduced Sylvain Marveaux for the final 15 minutes and his injection of pace added to Newcastle's potency in attack.
His 84th-minute cross found its way to Ba who, after mis-kicking his first effort, forced a low save out of Cech from eight yards.
With 90 minutes on the clock Luiz required treatment following a clash of heads with Ba as the two contested another Marveaux cross.
Despite requiring a bandage after suffering a nasty cut, the Brazilian defender was untroubled for the five minutes of additional time as Chelsea saw out the remainder of the game without incident.