Wenger's men saw off their opponents in a fine team display that never looked in doubt, forcing Given into making a number of good saves and topping it off with a clean sheet.
The Gunners were dominant in the first half and took the lead when Kieran Gibbs netted his first-ever Premier League goal thanks to an unconvincing attempt of a save from Shay Given.
Theo Walcott doubled the score later in the half before a confident display in the second which brought a third from a Mikel Arteta free kick.
Gervinho returned for the home side in his first league start since returning from the African Cup of Nations, leaving Aaron Ramsey to drop to the bench.
As for the visitors, Alex McLeish went with Emile Heskey and Gabriel Agbonlahor to lead the line with the match-winner against Fulham, Andreas Weimann, left out. Charles N'Zogbia was still missing with a knee problem.
Wenger was dealt an early blow before kickoff when Laurent Koscielny injured himself in the warmup. Johan Djourou replaced him in the lineup.
Things got worse for the Gunners' boss when the Swiss defender himself was then down for a prolonged period, just three minutes in, after a challenge with Emile Heskey left him with a blood stained jersey. However the 25-year-old played on after getting a new shirt.
When play got flowing, it was a usual day at the office for the Gunners, who dominated opening spells of possession at the Emirates, although the visitors mustered the first chance after a swift counterattack from an Arsenal corner. Marc Albrighton rushed clear, as Villa had three on two, but smashed his effort high and wide.
From then on though it was very much one way traffic.
Great work from Bacary Sagna and Walcott on the right flank saw the fullback advance forward before finding Robin van Persie in the box. The Dutchman flicked it with his heel into the path on Walcott, who had continued run, but the winger's shot was straight at Given. Sagna lashed the follow up wide.
The deadlock was broken rather easily for Arsenal after quarter of an hour, Gibbs received the ball from Gervinho inside the opponents' box, he was given far too much room and was allowed to hit it with the ball slipping under the Villa keeper, who will feel he should have done better.
And it wasn't long before the hosts doubled their lead.
Carlos Cuellar gifted the ball to Alex Song with a poor pass from the back. The Cameroon midfielder then found Walcott with a delightful ball over the top before the winger controlled wonderfully and produced a calm finish 25 minutes in.
That second goal signaled a period of meltdown for Mcleish's men.
A minute later Thomas Vermaelen fired a low cross towards Van Persie, who, in his current form, you would have backed to score but he caught it with his shin and missed the target.
Then, Given was forced into a top save from Arteta, the Irish keeper doing well to tip over the Spaniard's long-range drive.
Villa did manage to get a slight foothold in the game after that, seeing its share of possession rise. But it was Arsenal which conjured up the last chance of the half.
With just over five minutes until the break, Song played Van Persie in beyond the visitors' defense. Initially the ball got stuck under his boots, but a lovely drawback helped the captain beat a scrambling Given presenting him with an open goal. However, the striker was denied by some brilliant positioning from Stephen Warnock, who blocked his shot off the line.
Villa looked more lively at the start of the second half but failed to create any real chances, although it did have a shout for a penalty turned down when Agbonlahor appealed for handball from Djourou.
The 15 minutes after the restart were open but didn't bring any clear chances.
Gary Gardner brought down Tomas Rosicky in a dangerous area but Arteta's free kick hit the wall. Wojciech Szczesny then gave the ball straight to Villa when trying to launch a quick move, before catching the cross and managing to successfully start a counterattack but Gervinho's end cross was too far ahead of his team-mates.
Arsenal looked very happy to just keep the ball as the hour mark approached and the home crowd certainly appreciated a lovely bit of showboating from Van Persie as he teased James Collins on the left flank.
Rosicky, then had two decent chances in the space of five minutes. Firstly Gibbs whipped in a cross from the left with the ball falling to the Czech midfielder after Walcott was beaten in air, but his volley was deflected wide.
The second effort forced another decent stop from Given, the 31-year-old's swerving effort parried away by the keeper.
Villa had a golden opportunity to get back into the match. With 20 minutes left, Andre Santos gave the ball to Weimann with his first touch of the game, but the visitors' substitute crossed to no one when shooting himself would have been a better option.
Arteta was next in line to test Given, but his free kick from a wide left position was tipped over by the 35-year-old - although no corner was awarded. Steven Ireland giving away the foul when on a booking, after a jinxing run from the lively Walcott.
And lining up they were, Aaron Ramsey then fired a low shot towards goal after a neat turn away from his man. However, the shot went narrowly wide of the mark.
Alex Oxlade-Chamberlain was introduced with just over 10 minutes to play and was convinced he should have had a penalty after a lunge from Ireland. The winger accelerated through the gears down the right before the Villa man lunged it right on the edge of the box, but replays showed he got the ball.
Weimann had one final chance for the visitors as the ball fell to him behind the defense. The forward hesitated though and allowed Djourou to get back and block the shot.
The Gunners then rubbed salt in the wounds by adding a late third in stoppage time with a fantastic free kick from Arteta that left Given with no chance.
The result sees Wenger's men go three points ahead of bitter rival Tottenham, which drew 0-0 with Chelsea at Stamford Bridge earlier in the day, and eight points clear of Roberto Di Matteo's side in the race for fourth spot.