Arsenal already held a 2-1 lead at Craven Cottage with after two goals of real quality from Alexandre Lacazette, before Ramsey, just 38 seconds after stepping off the bench, made it three in sublime style.
Aubameyang completed the rout with a long-range drive in stoppage time.
Alexandre Lacazette sparked Arsenal's power surge at Craven Cottage, with his superb second-half strike restoring their lead after Andre Schurrle had cancelled out his opener.
Aubameyang sealed Arsenal's comfortable victory with two of his own 12 minutes later, as he capitalised on Hector Bellerin's assist in the 79th minute. "We knew Fulham play good football and play with a lot of counters, but I think the team played well".
Unai Emery's side, who have won every game since back-to-back losses to Manchester City and Chelsea in August, are now third in the table, above rivals Tottenham on goal difference.
- Both Ramsey and Aubameyang scored and assisted - this is the first time in Premier League history two substitutes have scored and assisted for a team in a single game.
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With Ramsey also providing a superb through ball to set up Aubameyang's second - and Arsenal's fifth - his contribution to the win was enormous, with all five of Arsenal's goals beautifully worked.
It was a significant statement of intent from a team widely written off ahead of Emery's first season in charge.
The move was reminiscent of Arsenal at the height of the Arsene Wenger era, as they countered at tremendous pace, en masse, with fantastic flicks and well-timed runs aplenty.
The Germany worldwide split the two Arsenal centre-backs and his deft lob from Vietto's slide-rule pass deservedly saw Fulham draw level just before the interval.
"I think with preparation they have the capacity to play a lot of matches. We will try to keep focus and continue to win games".
"I want to give them and to show them we are improving with our quality, with our mentality and above all with commitment we had here today".
"Our performance over the 90 minutes was very important".