Match ends, Stoke City 0, Everton 3.
Everton moved up to seventh after beating Stoke, who suffered a third successive Premier League defeat.
Romelu Lukaku put the visitors in front with a penalty after keeper Jack Butland had brought down Tom Cleverley.
Seamus Coleman headed in a Cleverley corner and Aaron Lennon intercepted a pass before slotting in as Everton went 3-0 up at the break.
Lukaku also had a header tipped on to the crossbar by Butland, while a poor Stoke struggled to create chances.
Cleverley and Barkley shine for Hodgson
A lot was made about Everton boss Roberto Martinez's dance moves at a Jason Derulo concert in the week, but it was his team impressing with their performance at the Britannia Stadium.
England manager Roy Hodgson was at the game and he will have liked what he saw from Toffees midfielders Cleverley and Ross Barkley.
The industrious Cleverley burst through before being brought down for Everton's penalty, while his delivery from corners was a constant threat and led to Coleman's goal.
Barkley's attacking instincts also played a part in the win and he could have had an assist when he crossed for Lukaku, whose header from close range was brilliantly saved by Butland.
"I thought we were very strong in every department," said Martinez. "Cleverley had a big influence in the game throughout."
Stoke continue slide in form
Stoke have endured a month to forget since their last league win against Norwich on 13 January.
Mark Hughes' side have been knocked out the Capital One Cup after a semi-final defeat on penalties by Liverpool, while they were beaten by Crystal Palace in the FA Cup.
The Potters have gained just one point from 12 in the league, dropping from seventh to 11th, and scored just one goal in six games.
The home side gave a debut to record £18.3m signing Gianelli Imbula but, like the rest of his team-mates, the midfielder struggled to make any kind of impact.
"I thought Imbila did OK. I felt sorry for him because as a debut that was a hard one to come into," said Hughes.
Man of the match - Tom Cleverley
Stoke boss Mark Hughes: "We huffed and puffed and didn't really create again and that is a concern for us.
"A disappointing day. We made mistakes at key times in the game and couldn't recover.
"We have to pick ourselves up and start doing the fundamentals and basics."
Everton manager Roberto Martinez: "We defended really well when we had to but the amount of opportunities we created is pleasing. If anything we should have scored three or four more in the second half.
"We have to make sure we don't drop our standards now."
The stats you need to know
- Romelu Lukaku has scored 16 Premier League goals this season, the joint-most by an Everton player in a single season along with Tony Cottee in 1993-94.
- Seamus Coleman scored his first Premier League goal since March 2015 and ended a run of 27 top-flight appearances without a goal.
- Aaron Lennon scored in three successive games [all competitions] for the first time in his career.
- Stoke have failed to score in four consecutive Premier League games for the first time and their worst run in the top-flight since March 1985 (eight games).
- Stoke have won a league-low one point in games that they have conceded the first goal in this season (11 games, W0 D1 L10).
Stoke's next game is at Bournemouth on 13 February, while Everton host West Brom on the same day with both games kicking off at 15:00 GMT.
- 14AfellaySubstituted forIrelandat 62'minutes
- 22ShaqiriSubstituted forOdemwingieat 62'minutes
- 18DioufBooked at 59mins
- 10ArnautovicSubstituted forJoseluat 76'minutes
- 25Funes Mori
- 16McCarthySubstituted forOsmanat 90'minutes
- 20BarkleySubstituted forMirallasat 87'minutes
- 10LukakuSubstituted forKonéat 76'minutes
- Andre Marriner
- Shots on Target
Second Half ends, Stoke City 0, Everton 3.
Attempt saved. Mame Biram Diouf (Stoke City) header from the right side of the six yard box is saved in the centre of the goal. Assisted by Joselu with a cross.
Foul by Peter Odemwingie (Stoke City).
Bryan Oviedo (Everton) wins a free kick on the left wing.
Substitution, Everton. Leon Osman replaces James McCarthy.
Corner, Everton. Conceded by Marc Muniesa.
Substitution, Everton. Kevin Mirallas replaces Ross Barkley.
Attempt missed. Stephen Ireland (Stoke City) right footed shot from outside the box is too high. Assisted by Joselu.
Corner, Stoke City. Conceded by Phil Jagielka.
Offside, Stoke City. Joselu tries a through ball, but Glen Johnson is caught offside.
Attempt missed. Ramiro Funes Mori (Everton) header from the centre of the box misses to the right. Assisted by Tom Cleverley with a cross.
Corner, Everton. Conceded by Jack Butland.
Attempt saved. Arouna Koné (Everton) right footed shot from the centre of the box is saved in the bottom left corner. Assisted by Ross Barkley.
Substitution, Stoke City. Joselu replaces Marko Arnautovic.
Substitution, Everton. Arouna Koné replaces Romelu Lukaku.
Giannelli Imbula (Stoke City) wins a free kick in the defensive half.
Foul by Gareth Barry (Everton).
Corner, Stoke City. Conceded by Ramiro Funes Mori.
Attempt blocked. Giannelli Imbula (Stoke City) left footed shot from the centre of the box is blocked. Assisted by Stephen Ireland.