After a dreadful start to the season, Mikel Arteta's side are now up to 10th place in the league and they never looked in danger against a Newcastle side that looks demoralised.
Aubameyang struck the post in the first half and Alexandre Lacazette forced a good save out of the Newcastle keeper just after the interval.
But Aubameyang finally fired the Gunners ahead in the 50th minute, finishing off a counter-attack, running at the Newcastle defence and then blasting home a powerful left-foot drive at the near post.
Ten minutes later Bukayo Saka made it 2-0 with a confident slot home after good work down the left flank from impressive youngster Emile Smith Rowe, who jinked his way around the back of the Newcastle defence before delivering a pinpoint pass.
Aubameyang completed the comfortable victory after Cedric Soares got to the byline and pulled the ball back into his path.
VAR examined whether the ball had crossed the line before Cedric's pass but allowed the goal to stand. Arsenal have now kept a clean sheet in five straight games in all competitions.
"I'm really happy overall. Really positive performance, collective and individually we looked really solid and convincing from the first whistle," said Arteta.
"It took us a little bit longer than I expected to score the first goal but I really like the chemistry, cohesion and rhythm the team played with."
Aubameyang had only netted three goals prior to Monday's game and his manager was delighted to see him score his first double since last season's FA Cup final.
"He needed that for his confidence and the team needs that to be successful. We need him at his best. We were missing his goals, we all know that so to have them back is great for the team," he said.
Newcastle boss Steve Bruce had made eight changes to his team after the defeat to bottom club Sheffield United and was disappointed his team could not improve on a solid first half.
"We gave as good as we got and got into ourselves some decent opportunities but that little bit of confidence has ebbed away for sure. We were caught in the second half where we didn't see it coming from the first-half performance," he said.
Asked about his future, the experienced Bruce said: "I am trying to do the best I possibly can as always but you will have to ask others about that."