The Welsh midfielder netted two of his side's four first-half goals and rounded off the scoring 74 minutes in, as the Gunners returned to winning ways and reduced the gap on the top four to five points.
There was also a hat-trick of a different kind for Henrikh Mkhitaryan, marking his first home start with three assists - one of which was for Pierre-Emerick Aubameyang, who was also left smiling on his Arsenal bow.
The first of Arsenal's four first-half goals arrived through their first attempt of note, as star attacking trio Mesut Ozil, Aubameyang and Mkhitaryan exchanged passes, before the latter teed up Ramsey to convert from close range.
Fresh from claiming his first assist in an Arsenal shirt, Armenian playmaker Mkhitaryan then sent a long-range shot inches wide of the opposition target.
Ramsey doubled his own personal tally for the evening 19 minutes in, this time from further out as he profited from time and space to send a deflected effort flying past Jordan Pickford.
Having conceded from all three shots on target, Everton finally managed to get the ball into the other half of the field and could have had a lifeline when Cuco Martina miscued his volley.
A decent opening also came and went for Theo Walcott on his return to the Emirates Stadium, delaying a shot and seeing it blocked by the covering Mustafi, and Arsenal soon moved back through the gears.
Debutant Aubameyang was denied down low by Pickford after being spotted by Ozil, with the angle proving too much to overcome, but he found a way through six minutes later after latching on to a Mkhitaryan through-ball.
A delicate clipped finish got the Gabonese striker off the mark with his first goal in an Arsenal shirt, though he was well offside when the pass was made.
There could well have been a fifth before the interval, only for Nacho Monreal's downward header to come back off the crossbar and deny him a third goal in four games.
Arsenal, who also led by four goals at half time in their last home outing, were grateful to the woodwork for momentarily keeping their clean sheet intact early in the second period.
Oumar Niasse should have done better when prodding against the post at the end of a delightful Walcott cross, and normal service soon resumed as Mkhitaryan tested Pickford from the next attacking move.
Everton did manage to get a foothold of sorts in the contest 64 minutes in, with young forward Dominic Calvert-Lewin coming off the bench to reduce the arrears with his headed goal soon after being introduced.
The four-goal margin was restored before the game was out, though, and it was a big moment for Ramsey as he tucked the ball past Pickford from his final touch of the evening - Mkhitaryan again claiming the assist on an evening when it all went right for Arsenal.
ARSENAL (4-2-3-1): Cech (Ospina 70'); Bellerin, Koscielny, Mustafi, Monreal (Kolasinac 46'); Xhaka, Ramsey (Wilshere 75'); Iwobi, Mkhitaryan, Ozil; Aubameyang
EVERTON (3-4-3): Pickford; Mangala, Keane (Davies 46'), Ashley Williams; Cuco Martina, Gueye, Schneiderlin, Kenny; Walcott (Calvert-Lewin 61'), Niasse (Tosun 78'), Bolasie