After a Saturday of making up points for the Gunners, they find themselves just one point behind Everton and Tottenham (though the latter have a game in hand) and five points behind Chelsea in third.
A late, deflected free kick by Lukas Podolski broke the deadlock, giving Arsenal a strong start to February.
The Gunners dictated the flow of the match with 66 percent of possession and 23 attempts on goal. The game also saw Mikel Arteta return from injury back into his role of defensive midfielder, pushing Jack Wilshere further up the pitch.
Here are six talking points from the match.
Most of the talk was about Ignacio "Nacho" Monreal, the Gunners' only signing of the January transfer window.
The Spaniard made his first start in an Arsenal jersey on Saturday, playing as the left-back due to Kieran Gibbs' injury.
Overall, Monreal's performance was neither hugely positive nor negative—he didn't have a lot of defending to do. He was purchased because Gibbs' backup, Andre Santos, lacks the defensive skills to start.
Monreal's four clearances, 45 completed passes (25 of them in Stoke's final third), one key pass, three aerial duels won and two interceptions showed viewers that he can be a good all-around left-back (stats from Arseblog).
Nacho's main negative involvement, in my memory, was a disastrous shot from a long way out that skewed way wide, close to resulting in a throw-in.
So we don't have much conclusive evidence that can tell us a lot about the 26-year-old.
But he will definitely be tested in coming weeks.
Alex Oxlade-Chamberlain got a surprise start over Lukas Podolski on the left flank.
The young Englishman was very influential on the tempo of the game, using his speed to get by Stoke defenders.
However, what I will remember from the Ox's performance are a couple of great opportunities that he passed up in the first half.
One of them was an off ball that somehow reached him following a corner. "Ox-Chambo" controlled it nicely but wasn't able to aim the shot properly, hitting Asmir Begovic in the center of the goal from a very short distance.
The other came from a brilliant through ball played by Jack Wilshere in between two Stoke defenders. Oxlade-Chamberlain, who only had one touch to shoot, opened his body and tried to curl the ball toward the far post. It was, however, saved by Begovic's outstretched left hand.
It was a very makeable chance, although I wouldn't go so far as to call it a sitter.
He has scored some very nice goals in the past, but the youngster needs to work a little bit on his finishing.
Ryan Shawcross, who infamously shattered Aaron Ramsey's leg in 2010, had another horrible challenge, but this time it was on Laurent Koscielny.
It was a 50-50 ball that Koscielny managed to reach first, and being a little late, Shawcross' studs drove into the Frenchman's crotch.
It looked very painful, and the actions of the Stoke center-back, who only received a yellow card, were not well-received by Wenger. From The Telegraph:
It looked to me [like it should have been a red card] but I have to look at it again as I am maybe not completely objective when it comes to Ryan Shawcross.
The incident involving Michael Owen and Mikel Arteta occurred very late in the game.
Arteta put in a very hard challenge on Owen, getting the legs of the Englishman during his follow-through. Owen then punched Arteta from behind, and that's when things got a bit rough.
Wilshere immediately jumped in to defend his teammate, giving Owen a shove, which caused the two to exchange what must have been harsh words.
Wilshere brings fire, spirit and fight to the Arsenal squad like no one else. And that is wonderful: Every team needs someone to be a little physical every now and then.
But the Gunners' No. 10 can go a little over the top sometimes.
So far, Wilshere doesn't have a whole lot of yellow cards, but he needs to be careful with his physical retaliation because he can get in some serious trouble.
Ah, the criticism of Theo Walcott.
For this part, let's focus on the relevant stuff because Walcott's game is insulted and put down constantly by all kinds of people.
But Walcott is, and has always been, a fairly predictable player on the right flank. It's no secret that he loves going to his right and has trouble on his left foot.
Even so, he proved to be a huge threat against Stoke, even when the defenders knew his main tendency.
The speedster had a few great turn-and-go touches with his back to the defense, giving himself room to run. In my opinion, he was even the man of the match.
Of course, a few wayward balls are to be expected from all players, so we can't criticize Walcott in that department.
It seems that Walcott has really been working on his first touch, and as a result, he had a very impressive performance.
Some people don't like 1-0 wins, but I love them. You have to embrace the occasional "One Nil to the Arsenal."
Watching Manchester United is infuriating for the Arsenal supporter. Even when they aren't playing their best or don't have any flair to a win, the bottom line remains: They win.
If you turn on the television and see Sir Alex's side down a goal, you know they will come back. If you happen to come across a 0-0 in the 60th minute, you know they will snatch a late goal and eke out a win.
And winning a solid one of those matches should give you confidence. It may not give you the joy of a 7-3 win, but if you really earned a 1-0 win as the Gunners did on Saturday, there's some good self-belief coming your way.
Following a fairly disappointing 2-2 draw against Liverpool, this is a good result that could change Arsenal's mentality. After horrible defending on Wednesday, a clean sheet is exactly the right way to bounce back.
This game will undoubtedly help the Gunners, which are now trying to get back into the top four.