Beaten by Brentford and Chelsea in their first two Premier League games, Arsenal arrived at the Hawthorns in turmoil after their worst ever start to a season.
Mikel Arteta's side were booed off following Sunday's 2-0 home defeat against Chelsea, with a group of supporters surrounding the Arsenal manager's car and chanting for him to quit as he drove away from the stadium.
Against that miserable backdrop, Arteta could not afford a defeat against Championship promotion chasers West Brom, who rested their entire first team and fielded a side with seven debutants.
Fortunately for Arteta, Aubameyang was able to make his first start this season after recovering from the coronavirus.
Aubameyang scored Arsenal's first two goals of the campaign before Nicolas Pepe and Bukayo Saka netted.
The Gabon forward completed his treble just after the hour and Alexandre Lacazette added the sixth.
It won't buy Arteta much breathing space however as this weekend they face a daunting trip to Premier League champions Manchester City, where Arteta worked as Pep Guardiola's assistant before joining Arsenal.
Losing to City would pile more pressure on Arteta, who has pleaded with Arsenal's fans to back the team during a difficult period he describes as "unprecedented" in the club's history.
Amid reports former Inter Milan boss Antonio Conte is being lined up to replace Arteta if results don't improve in the next five games, he desperately needed a morale-boosting victory against Albion.
There was no lack of support for Arteta from Arsenal's sizeable support in the midlands and, for once, his players delivered as well.
Having failed to qualify for Europe, Arsenal were forced to enter the League Cup in the second round for the first time since 1995.
The north Londoners hadn't suffered a second round defeat in the competition since 1978 and they kept that run intact.
Arsenal looked vulnerable early on and it took a fine save from Aaron Ramsdale, making his debut after his move from Sheffield United, to keep out Taylor Gardner-Hickman's low strike.
Adam Reach fired narrowly wide of the far post from the resulting corner, but Arsenal were gifted the lead in the 17th minute.
Woeful Albion defending on the edge of their own area presented the ball to Saka and when his stinging effort was pushed out by Alex Palmer, Aubameyang was on hand to tap into the empty net.
Arsenal had too much experience for Albion's callow youngsters and their captain struck again in the 45th minute.
Pepe beat the offside trap and when his shot hit the post, Aubameyang was waiting to slot home from close-range.
Pepe bagged Arsenal's third seconds before the interval, the Ivory Coast winger stretching to score from four yards after Aubameyang's shot was saved.
Saka made it four in the 50th minute with a sweeping finish from Martin Odegaard's backheeled pass.
Aubameyang sealed his third Arsenal hat-trick in the 62nd minute when he curled into the far corner from the edge of the area.
Lacazette came on for his first appearance this season and rifled home from Pepe's 69th minute cross.
Southampton crushed fourth tier Newport 8-0, with Mohamed Elyounoussi scoring a hat-trick in the biggest away win in the club's 136-year history.
Burnley beat Newcastle 4-3 on penalties after a 0-0 draw at St James' Park.