Aubameyang, who had earlier hit the post from a tight angle in the first half, opened the scoring in the 50th minute when he fired past Newcastle goalkeeper Karl Darlow.
Arsenal doubled their lead as Emile Smith Rowe’s pullback found Bukayo Saka and the England international side-footed the ball into the net.
Aubameyang, 31, got his second and the Gunners’ third after Cedric Soares, in his first league start of the season, got to the byline and set up the striker.
The Gabon international scored 29 goals in all competitions last season, including 22 in the Premier League, but he had previously struggled for goals in 2020-21.
This double took his league total to five for the campaign and boss Mikel Arteta was pleased to see Aubameyang return to form.
“He needed that for his confidence and the team needs that to be successful,” said the Gunners manager.
“We were missing his goals, we all know that, so to have them back is great for the team.”
Miguel Almiron had Newcastle’s best chance but shot over from the edge of the penalty area when it was goalless.
The victory takes Arsenal above Aston Villa into 10th, with the Gunners seven points adrift of fourth-placed Liverpool in the last Champions League qualifying spot.
Newcastle are 15th, seven points clear of 18th-placed Fulham, although the London side have a game in hand.
For Bruce, who faced calls for his resignation after last week’s 1-0 loss to bottom-of-the-table Sheffield United, his side have now not won in nine matches in all competitions.
Arsenal are in danger of having their worst Premier League season since 1994-95 when they finished 12th – the last time they failed to qualify for European football.
After Mikel Arteta replaced Unai Emery in December 2019, the Gunners finished eighth last season, although they did win the FA Cup in August.
Despite 2020-21 having been a tough campaign for them so far, there have been recent signs of revival and this win extends their unbeaten run to six matches.
They dominated possession at Emirates Stadium and should have taken a 14th-minute lead. Smith Rowe did well to release Saka and his low cross found Aubameyang, but, off balance and from a tight angle, he could only hit the post with the goal unguarded.
Aubameyang twice more failed to hit the target when well placed and David Luiz should have done better with a free header.
But it only took five minutes of the second half to make a breakthrough as Thomas Partey’s pass forward let Aubameyang run at the Newcastle defence from the halfway line and he blasted in only his second league goal in 10 games.
It became 2-0 10 minutes later when Smith Rowe did well down the left flank and his pass helped Saka score for the third time in six matches.
Soares then made a fine run down the opposite wing and his pullback was steered into the net by Aubameyang, whose return to goalscoring form is a massive boost for the Gunners.