Mikel Arteta's Gunners, brimming with confidence after their 6-0 hammering of Lens in the Champions League in midweek, raced into a 2-0 lead at the Emirates within 13 minutes.
Bukayo Saka opened the scoring and Arsenal doubled their lead when Oleksandr Zinchenko cut the ball back for Martin Odegaard, who picked out the bottom corner.
The home side came agonisingly close to a third goal when Gabriel Martinelli cannoned a shot off the post towards the end of the first half.
But they failed to put the game to bed and were made to sweat when Wolves forward Matheus Cunha found the top corner in the 86th minute to set up a tense finale.
Despite the scare, Arsenal, last year's runners-up, held on for their 10th win in 14 league games, which moves them four points clear of champions Manchester City, who host Tottenham on Sunday.
Five-star Burnley
Vincent Kompany's Burnley hammered fellow strugglers Sheffield United 5-0 at Turf Moor.
Jay Rodriguez fired the home side ahead with just 15 seconds on the clock -- the fastest goal of the season so far.
Jacob Bruun Larsen extended their lead shortly afterwards, racing onto Dara O'Shea's long ball down the right and keeping his composure to slot past goalkeeper Wes Foderingham.
Sheffield United's task was made almost impossible when Oli McBurnie received a second yellow card for a foul on O'Shea late in the first period.
Zeki Amdouni made it 3-0 in the 73rd minute with Luca Koleosho and Josh Brownhill also finding the net as the floodgates opened.
Paul Heckingbottom's men are stuck on just a single win and have now conceded five goals or more on three occasions this season.
But Burnley are now just two points behind 17th-placed Luton after just their second win of the season.
Luton went down 3-1 at Brentford, where Neal Maupay opened the scoring from close range early in the second half and Ben Mee made it two.
Luton substitute Jacob Brown rifled a shot low beyond Mark Flekken in the 76th minute but Shandon Baptiste restored Brentford's two-goal cushion just five minutes later.
Everton, in action against Nottingham Forest later on Saturday, are now bottom of the league, due to a swingeing 10-point deduction imposed for breaking Premier League financial rules.
Despite their predicament, Sean Dyche's men will be confident they can secure a third consecutive away win in the league.
In the late match, Newcastle face Manchester United at St James' Park, where a win for either side would lift them to fifth place in the table at the expense of Tottenham.
United have won five of their past six league games after a terrible start to the season but goalkeeper Andre Onana will be in the spotlight after costly errors in his team's 3-3 draw at Galatasary in midweek.
