The Toffees grabbed the lead in the 11th minute as Romelu Lukaku's penalty took him to 20 goals for the campaign.
A Seamus Coleman header then extended the advantage in the 28th minute, and with Aaron Lennon punishing a Philipp Wollscheid error to add a third for the visitors in the 42nd, Roberto Martinez's men looked to have wrapped things up before the interval.
Things could have been even worse after the break for a lacklustre Stoke side, with the efforts of their goalkeeper Jack Butland - including tipping a Lukaku header onto the bar - key in ensuring they sustained no further damage.
Everton have been accused of underachieving this term, but this was impressive stuff from the Merseyside outfit, who, having built upon their 3-0 win over Newcastle on Wednesday, are up to seventh in the table.
Stoke, in contrast, were abject
They were looking for home comfort here, returning to playing at their own ground following a run of four straight matches on the road that had seen them beaten at Leicester and Manchester United in the league and exit two cups.
But with them slipping to what was their third straight 3-0 league loss and down to 11th in the table, their fans will be concerned about their campaign, so impressive for so long, now fizzling out.
Everton were positive from the off and were awarded the early spot-kick when Tom Cleverley latched on to Bryan Oviedo's through-ball and went down in the box as Butland made contact while coming out to meet the former Manchester United midfielder.
Lukaku stepped up and calmly sent the penalty down the middle to put his team in front.
Stoke struggled to respond and it came as little surprise when Coleman made it 2-0, showing great desire to beat his marker Erik Pieters and connect with Cleverley's corner to nod past Butland.
At the other end, Mame Diouf glanced a header wide and Stoke's new record signing Giannelli Imbula fired into the stand.
But the hosts then shot themselves in the foot as Lennon collected a misplaced ball from Wollscheid and burst through before producing a slotted finish.
Everton almost scored again just before the hour mark, with Butland pulling off a great save to divert Lukaku's header against the woodwork.
Lukaku was subsequently denied twice in quick succession by a Marc Muniesa block and another fine Butland save.
And after James McCarthy cracked a shot just wide of his goal, Butland - watched from the stands by his England boss Roy Hodgson - then did well once again to keep out an effort from substitute Arouna Kone.
Those heroics will have been of little comfort to Stoke manager Mark Hughes, whose side continued to offer little in attack and were booed by some of the home fans at the final whistle.
TWEET OF THE MATCH
Former Everton man Anders Limpar (@Anders_Limpar): "The Blues are doing the Derulo dance on Britannia! ?
Love it! ??? #COYB"
PLAYER RATINGS
STOKE
Jack Butland: 7 (out of 10)
Glen Johnson: 5
Philipp Wollscheid: 4
Marc Muniesa: 5
Erik Pieters: 5
Glenn Whelan: 5
Giannelli Imbula: 7
Xherdan Shaqiri: 5
Ibrahim Afellay: 5
Marko Arnautovic: 5
Mame Diouf: 5
Subs:
Peter Odemwingie: 5
Stephen Ireland: 5
Joselu: 5
Everton
Joel Robles: 6
Seamus Coleman: 7
Phil Jagielka: 6
Ramiro Funes Mori: 6
Bryan Oviedo: 7
James McCarthy: 7
Gareth Barry: 6
Aaron Lennon: 8
Ross Barkley: 7
Tom Cleverley: 8
Romelu Lukaku: 7
Subs:
Arouna Kone: 6
Kevin Mirallas: 6
Leon Osman: 6
STAR MAN
Aaron Lennon: The Everton winger's return to form continues, with another lively display and his third goal in three games in all competitions.
MOMENT OF THE MATCH
Philipp Wollscheid's error and the ruthless finish from Lennon that followed summed up the whole match - and was the point at which both sides must have known which way it was going to end up.
VIEW FROM THE BENCH
Everton boss Roberto Martinez has taken some flak this season, but there was real evidence here that his team are turning a corner as they notched a third straight 3-0 win in all competitions
At half time he must have felt like doing a jig similar to that he was shown performing at a Jason Derulo concert in the footage that emerged earlier this week.
Opposite number Mark Hughes, on the other hand, may well be worried as his team's poor sequence of results continues
This was not just a flat performance by Stoke, like against Manchester United on Tuesday - it was a really poor one.
MOAN OF THE MATCH
The weather
Rarely have the conditions been more grim at Stoke than this, and Everton must be commended for putting on a great show amid the fierce wind and rain.
WHO'S UP NEXT?
Everton v West Brom (Barclays Premier League, February 13)
Bournemouth v Stoke (Barclays Premier League, February 13)
Source : PA
Source: PA