The result leaves the Toffees just six points clear of the relegation zone.
Read how all the action unfolded below.
Good evening! It's an hour until action gets underway at the Britannia Stadium, where Stoke City will be hoping that their strong recent form will continue against a struggling Everton side. The team news is just out, so let's take a look at the squads.
STOKE STARTING XI: Begovic, Bardsley, Wollscheid, Wilson, Pieters, Nzonzi, Whelan, Walters, Adam, Moses, Crouch
EVERTON STARTING XI: Howard, Garbutt, Stones, Jagielka, Coleman, Barry, McCarthy, Gibson, Lennon, Naismith, Lukaku
STOKE SUBSTITUTES: Butland, Arnautovic, Diouf, Cameron, Sidwell, Teixeira, Shenton
EVERTON SUBSTITUTES: Joel, Kone, Mirallas, Besic, Barkley, Osman, Alcaraz
So there are two changes for the hosts following their win over Hull City at the weekend. Stephen Ireland misses out with the nasty cut leg that forced him out at half time on Saturday, with Charlie Adam coming in in his place. Meanwhile, Peter Crouch returns in place of Mame Biram Diouf.
Meanwhile, the visitors make three changes to the side that started the 2-0 defeat to Arsenal on Saturday. Darron Gibson, Steven Naismith and Aaron Lennon all return to the starting lineup, while Mirallas, Besic and Barkley all drop to the bench.
11 points separate these two sides ahead of kickoff, which equates to four places in the table. Everton are just six points clear of the relegation zone, and have played a game more than 18th-placed QPR, so really need the three points to make sure that they're not dragged into the relegation battle. By contrast, a victory for Stoke tonight could move them as high as eighth.
Here's a look at the stadium just a few minutes ago:
Stoke have won four of their last six matches in the league, with their only defeat coming at the hands of Manchester City last month. Everton's only win in their last 11 matches was a narrow 1-0 win over Crystal Palace.
Having come off the bench against Hull at the weekend, Peter Crouch scored his 46th headed goal, tying Alan Shearer's record for most headed goals in the Premier League. Should the tall forward nod another in tonight, the record will be his outright.
Stoke have a chance to record a league double over Everton for the first time since the 1966-67 campaign, having already beaten the Toffees at Goodison Park this season. The last three matches between these two sides at the Britannia Stadium have ended 1-1.
Ahead of this match, manager Roberto Martinez told reporters: "The stats can be used in any way you want. Domestically in the last nine games we only lost two, Chelsea and Arsenal, and the first in the last minute in a very sad manner against the league leaders. We are going to try and get as many points as we can and try and build some momentum. We are coming off the back of a disappointing result, but not a disappointing performance at Arsenal. It is an important game and a vital three points. It has been a big learning curve for everyone. It is a learning curve for how to perform consistently and get consistent results. It has been a demanding period but it will be helpful for our future."
Meanwhile, Mark Hughes said in his pre-match press conference: "We weren't anticipating challenging [for Europe] this season, but given the fact that we are in a good position, we have good games coming up then you never know. Sides who started brightly, like Southampton, they have fallen back a little bit and we have gained some momentum. If we continue to play as well as we have done and those teams slip up then we are ready to get in there."
With the FA Cup returning this weekend, neither of these two sides will be playing again at the weekend. Stoke have a 10-day break after this match as they visit West Brom, while Everton return in the Europa League next Thursday against Dynamo Kiev.
REFEREE WATCH! It will be Mark Clattenburg officiating this evening's match. He oversaw Everton's win over West Ham earlier in the season, but has not taken charge of a Stoke match so far this campaign.
We have live coverage of all seven Premier League fixtures taking place this evening, as well as a couple of European ties. You can find links to all of our live commentaries here.
WEATHER! Just a quick update on the conditions at the Britannia this evening - it's a chilly 6C according to the latest forecast, but there's just a gental breeze and next to no chance of rain tonight, so it should be fine conditions for football.
It looked like Glenn Whelan injured his knee during the warmups a short time ago and was seeking attention from the physio. The team haven't announced a change to their starting lineup yet though, so it looks like he'll still be involved.
PREDICTION! With kickoff fast approaching, it's time for a prediction. The form is certainly with Stoke heading into this match, but Everton will surely make it difficult for the hosts. Regardless, I'm going for a 2-1 win this evening.
Here are the Everton boys heading out for their warmup earlier. The teams will be heading back out any minute:
The players are making their way out ready for kickoff in front of a packed Britannia Stadium.
KICKOFF! Everton get the action underway.
Stoke win an early free kick when Barry trips Adam in midfield. Wilson launches it deep looking for Peter Crouch, but he can't quite get on the ball for nod in a quick goal for the hosts. It's a bright start by the Potters though.
CHANCE! The home side have another free kick, this time near the corner flag. Walters curls it in for Bardsley, but his powerful strike is blocked before it can test Tim Howard.
After a bright start by the hosts, Everton are starting to attack as Jagielka and McCarthy try to get the ball down the left flank, but it's blocked by Pieters, who quickly races down the other end on the counter, but Howard claims it.
PENALTY APPEAL! The home side want a penalty after N'Zonzi is brought down on the edge of the box by Gibson, but Mark Clattenburg says that it was a fair challenge and waves for both sides to play on.
Naismith earns himself a talking to from the referee as he gives away a third free kick of the evening while Everton are on the attack. There was little in it as he collided with Pieters, but he'll have to be careful not to pick up an early booking.
CHANCE! Darron Gibson finds himself in space on the edge of the box as Garbutt plays the ball through to the midfielder, but his low strike is straight at Begovic, who easily gathers.
BOOKING! Gareth Barry charges into Charlie Adam, not for the first time this evening, and he picks up the match's first yellow card.
SUB! It's an early change for the home side as Phillip Wollscheid picks up a knock after being tackled by John Stones, forcing Geoff Cameron to come off the bench early for Stoke.
Everton have certainly been the more attacking after a strong start by the home side, but a long ball forward from Jagielka that's flicked on by Naismith doesn't quite fall for Lukaku, who hasn't seen too much action so far.
Lukaku finally has an impact as he gets the ball out wide before squaring it to Naismith on the edge of the box, but the Scot soon found his path blocked by Whelan as he looked to get the shot away.
Moses and N'Zonzi get the ball down the other end as they try to set up Crouch after a quick counter from the home side, but the duo can't get the ball in from near the corner flag, leaving McCarthy to quickly head back down the other end. While both teams have been attacking, neither has really had a dominant spell yet, it's been pretty well matched.
Charlie Adam has been working hard in midfield so far and he battles again to try to create something for Crouch, but Jagielka is ready to intercept the pass and make the clearance for the visitors.
CHANCE! Probably the best chance of the match so far falls to Victory Moses, who from nowhere gets himself some space on the edge of the box, and he tries to rifle in what would have been a spectacular strike with some real power behind it, but Howard punches it clear.
GOAL! Stoke City 1-0 Everton (Victor Moses)
Just moments after almost firing the home side ahead, Victor Moses pops up again, and this time the ball is in the back of the net. Bardsley crosses it in, and the winger leaps up to nod it in. He's not a regular header target, but he certainly took that one well to head into the top corner.
Garbutt launches a throw deep down field as Everton try to respond. Walters wins it back for the home side though and is away down the other end looking for Crouch, but Stones is ready to block it.
Stoke are really looking dangerous on the counter-attack as a blocked Gibson effort is taken down the other end by the hosts. After a couple of balls into the box are cleared, before a Bardsley delivery is claimed by Howard. Incidentally, this is the 11th time Everton have let the first goal in in the Premier League this season, and on the 10 previous occasions they have gone on to lose.
Everton are continuing to launch long balls forward as they look for an equaliser before the break, but there's not that much organisation up front, with Lukaku having rarely got a touch, and Naismith often having to drop back to help get the ball back, while Stoke's defending has been excellent so far. Naismith does manage to get the ball up front, but Whelan is there to block.
CHANCE! Bardsley has been a real menace down the right flank so far and he's up again to provide another well-placed cross for Crouch, but Stones just gets to it first to nod it safely to Howard.
Stoke's defensive resolve is being tested in the final minutes of this first half as Coleman comes forward to lash a cross in intended for Lukaku, but Pieters has it blocked, while Naismith is crowded out.
CHANCE! Aaron Lennon finally finds a gap in the Stoke box to get a shot away, but his finish is an easy save for Begovic, who hasn't had too much to do so far.
HALF TIME: Stoke City 1-0 Everton
So at the break, Victor Moses's superb header separates the sides. Everton haven't been without their chances, but they haven't been sharp enough in the final third so far.
Here are some of the stats from the first half. Everton actually had more possession with 56%, and while both sides had five shots, three were on target for the visitors, which was one more than Stoke. The Toffees have been a bit scrappy though, conceding almost three times as many free kick as the hosts.
One of the main issues for Everton is that Lukaku has not been involved that often. The team's record-signing has been closely marked by Wilson and Pieters, forcing the team to look elsewhere with their crosses into the box.
The only yellow card in the first half went to Gareth Barry, despite Steven Naismith catching referee Mark Clattenburg's eye as well. The booking is a costly one for the midfielder, as it's his 10th of the season so he'll miss their next two outings.
The players are heading back out ready for the second half.
RESTART! Stoke get the second half underway.
The home side are piling on the pressure early in the second half, forcing Garbutt to concede a corner. Adam's delivery into the box is superb, but there was no-one there to tap it in. The slightest of touches would surely have been enough for a second for Stoke then.
CHANCE! Having had little to do in the first half, Lukaku almost makes his mark at the start of this second half as he muscles his way into space on the edge of the box, before Cameron deflects his low strike just wide for a corner.
Lennon makes a speedy run towards the Stoke goal before finding his path blocked on the edge of the box. He squares it t Barry, but the midfielder can't create an opening either. It looks like whatever Roberto Martinez said to his players during the interval has had an impact though as Everton look much more threatening on the attack.
BOOKING! Naismith has given away a few fouls this evening, most of them on Bardsley, and Clattenburg has run out of patience, reaching for the yellow card as the striker goes in late on Bardsley.
After surviving something of a dominant patch from Everton, Stoke are back on the attack as Walters makes a charge down the right before attempting to cross it in for Crouch, but his delivery ends up going behind.
Everton force a free kick in a dangerous position when Pieters catches Lennon late. Garbutt has been on set piece duty tonight, and he continues, curling it in towards the penalty area, but it fails to clear the first man.
Lennon weaves around on the edge of the box before lofting the ball in towards Lukaku, but Cameron makes sure that the Belgian striker doesn't get to it. Meanwhile, it looks like the visitors could be making a change soon as they have a few of their subs warming up.
SUBS! It's a double change for the visitors as Arouna Kone takes the place of Aaron Lennon, while Gareth Barry makes way for Leon Osman.
Kone gets involved straight away, cutting back in from the left before passing to McCarthy, but the ball is eventually won back by Wilson, who launches Stoke on the counter.
CHANCE! Leon Osman has a shot blocked, but it falls to Kone, who take a touch before slicing it towards goal, forcing a reaction save from Begovic. The changes appear to have lifted Everton.
N'Zonzi shows his strength, racing down the left to reach a loose ball before shaking off a tackle from Garbutt to force a corner. Adam whips it back in with yet another superb delivery, but once again there's no-one there to convert.
SUB! Peter Crouch won't be breaking Shearer's header record tonight, as Mame Biram Diouf is on in his place.
Diouf tries to set up Moses for his second of the match, firing a through-ball for the winger, but there's just a bit too much on it, allowing Stones to get to it first.
Kone quickly gets involved as the ball heads down the other end, but he catches Walters to give away a free kick before he can get his shot away. Nothing seems to be going Everton's way tonight.
Moses is given absolutely ages on the edge of the box as he cuts from left to right looking to get a shot away. He passes to Diouf instead, who in turn cuts it back to Walters, but Everton manage to clear. There was absolutely no pressure on Moses though, despite the visitors having two defenders waiting for him to make a move.
It's a final change for the hosts as Arnautovic comes on in place of Charlie Adam, who really has worked hard for the hosts this evening.
Evertn pile forward as they continue to try to rescue a point, but Bardsley is back to help ensure that Stoke make the clearance. The hosts are just too tight at the back for Everton, despite the introdiction of the lively Kone and Osman earlier.
Stoke force a corner, and with Adam having gone off it's Moses to take it. He finds Pieters, but Howard eventually claims it to make sure Stoke don't double their lead.
Pieters thinks that he's got the ball to Diouf in a dangerous position, but the striker barges Stones out of way to make sure he's free, conceding a free kick. That would have been a good chance for the hosts, as the visitors didn't have too many players back to help out.
SUB! Everton make their final change, with Kevin Mirallas coming on for Steven Naismith in a bid to rescue a point for Everton.
GOAL! Stoke City 2-0 Everton (Mame Biram Diouf)
That's surely the win secured for Everton as Mame Biram Diouf uses all of his strength to stay on his feet on the edge of the box before passing to Arnautovic. The sub tries to squeeze it in from tight range, but it clatters back off the post. Luckily for the hosts, Diouf had followed him in, and lashed in the rebound.
CHANCES! Stoke are trying to finish with a flourish as Walters bursts in before Stones blocks his shot, but it's gathered by Moses, who curls it just wide of the top corner. Everton could find themselves letting a third in if they aren't careful.
Everton force a free kick in a decent position, in line with goal around 20 yards out. Mirallas lifts it over the wall, but it doesn't dip enough to trouble Begovic.
BOOKING! Begovic is rather leisurely taking the resulting goal kick, and he earns himself a yellow card.
Arnautovic is causing problems again, clearly wanting to make up for hitting the post earlier. He rounds a couple of defenders, but leaves himself with another tight angle, which he can't make. Meanwhile, there are to be four minutes of stoppage time.
BOOKING! Walters gets a yellow for tripping McCarthy just outside the box, although the midfielder is insistent that the tackle was in the area.
CHANCE! Garbutt continues with the set pieces, and this time he hits it superbly, but Begovic is equal to it, diving to his left to get it clear.
FULL TIME: Stoke City 2-0 Everton
Goals from Victor Moses and Mame Biram Diouf hand Stoke the win, giving them three straight victories for the first in the first time this season, also handing them a double over the Toffees.
The win lifts Stoke up to eighth in the table, while Everton stay 14th, just six points outside the relegation places.
Well that's all from this match, but join us again at the weekend when some of the sides not involved in the FA Cup are in Premier League action. Until then, thanks for joining me this evening. Goodbye.