The Gunners had victory wrapped up after 20 minutes thanks to Ramsey’s brace that started with an early goal assisted by Henrikh Mkhitaryan on his full Arsenal debut.
It was Theo Walcott’s return to the Emirates after making his January move to Goodison Park and the winger was the catalyst for the limited amount of Everton attacks.
Sam Allardyce’s side were abject from the start and only three tackles inside the first 45 minutes. In the build-up to the game, the Everton boss said he was looking for more consistency from his team following the midweek win against Leicester City but the only consistent pattern he got from his side was the Blues' inability to trouble teams away from home.
Dominic Calvert-Lewin headed home for the Blues with half an hour to go but it was little more than a consolation as Ramsey would complete his hat-trick.
Gunners romp to first-half lead
The hosts got started after six minutes with the Welsh midfielder getting the first of his three goals.
Mesut Özil flicked the ball wide to Mkhitaryan who played a ball across the Everton 18-yard-box. The waiting and unmarked Ramsey poked home past Jordan Pickford to give the Gunners the lead.
The Armenian, desperate for a goal for his new side, drilled a shot just wide of Pickford’s post minutes after the hosts take the lead.
However, the Gunners doubled their lead less than 10 minutes later.
Özil's corner was flicked on by Shkodran Mustafi and following a number of errors from the Everton back-line with Ashley Williams failing to win the header, Cuco Martina failing to clear and Eliaquim Mangala asleep, Koscielny was able to head home and double the visitors lead.
The German was left unmarked again on the left-hand side and teed up Alex Iwobi. The youngsters played in Ramsey and the Welshman was allowed to shoot from 25 yards.
His shot deflected off the debutant Mangala, wrongfooting Pickford and trebled the Gunners lead as the ball settles in the net behind the ‘keeper.
January signing Aubameyang, on his debut, got his first in Arsenal red 10 minutes before half-time. He was played in by his former Dortmund team-mate Mkhitaryan and despite being in an offside position, lifted the ball over a beaten Pickford.
Blues better but beaten
Everton started the second-half much brighter than the first with Tom Davies replacing Michael Keane and Allardyce changing his system to accommodate more in midfield.
The former England boss' attempt to play three in defence - after making five changes from midweek - had failed and was epitomised by a litany of errors from Keane, Mangala and Williams.
Davies' introduction gave the Blues an added boost of energy and he helped create chances for Walcott and Oumar Niasse but the Everton attack was unable to capitalise.
Niasse, cutting a lone figure up front, hit the post shortly after the half-time break but like Wednesday's win, he was unable to find the back of the net.
The returning Walcott was replaced by Calvert-Lewin and the young forward had an almost instant impact.
He headed home from Martina's cross but it was little more than the Blues salvaging a sliver of pride following their abject performance.
Ramsey completes his hat-trick
The Gunners answered back almost instantly when Ramsey, who was set to be replaced, again slotted home and low from a perfectly weighted ball from Mkhitaryan and completed his hat-trick.
Ramsey was replaced, to a standing ovation, by Jack Wilshere shortly after as the day belonged to the Welshman.