Arsenal manager Unai Emery urged Mesut Ozil to contribute more goals after the German's strike secured a third consecutive victory for his side and left Newcastle without a win.
Despite being frustrated in the first half, Granit Xhaka opened the scoring for the Gunners with an excellent long-range free-kick after the break, before Ozil followed up Alexandre Lacazette's blocked effort to double the advantage.
Ciaran Clark responded in stoppage time for the hosts, however Newcastle remain in a relegation place in the table with one win in their past 10 league games.
Ozil - making his 200th appearance for the club - ensured Arsenal won consecutive away league games for the first time since May 2017.
"His quality helps the team. It is important he scored. I want not only for him to assist, we need him to go in the box and score like today," said Emery - who had challenged the midfielder to "do more" before the game.
"I see the players are the same, each has quality. I will work with every player and continue our process to create the team as we want."
Meanwhile, Rafael Benitez's side remain on one point, equalling their worst return after five Premier League games - although they had much the better of the first-half chances as they pressed an Arsenal defence determined to build from the back.
The early pressure forced errors, as keeper Petr Cech passed the ball out for a corner and defender Shkodran Mustafi's stumble was indicative of an Arsenal back-line still trying to get comfortable with a new style of play under Emery.
However, Arsenal returned the stronger side after the interval and scored twice in 10 second half minutes to secure the points - despite a late Newcastle rally.
Following a tough start to Emery's reign, with opening league fixtures against champions Manchester City and Chelsea, victory at St James' Park is the Gunners third consecutive win and they now appear to be gaining some momentum under Arsene Wenger's successor.
Arsenal, who managed to see off a resurgent Cardiff prior to the international break, knew they would face a stern test against a Newcastle side that had adopted a defensive approach against Chelsea and Manchester City already this season - and were unable to settle into the match as the hosts pressed from the start.
Newcastle's first-half approach demonstrated exactly how to disrupt Arsenal's play under Emery, and both Cech and Mustafi in particular appeared hesitant on the ball under repeated pressure.
But the Gunners were able to take control of the game as the hosts' early energy faded - although it took Xhaka's sublime strike on 49 minutes to really give the visitors confidence.
Arsenal looked increasingly comfortable following Ozil's cool finish and were able to see the game out despite Clark's late reply as Emery's side continued to amend a poor recent away league record that had seen them lose eight of their last 10 prior to kick-off.
And it did appear, once they got into their stride, that Arsenal's players are adapting to Emery's philosophy - although on evidence there remains plenty of work to do.
"We are improving. We need to continue working individually and collectively to improve more things. In the first half we didn't control like we wanted but the second half we were better and the victory is just," said Spaniard Emery.
"We need to improve and score more individually. We need to work, every player - not only the attacking players but the midfielders and centre-backs from set-pieces."