The Germany international scored the opener before setting up his £16 million team-mate as Arsene Wenger's men blew away the hosts in a devastating three-minute flurry
Mesut Ozil, the subject of much criticism before the game, scored one and then assisted Danny Welbeck's first Gunners goal before Aly Cissokho put a third into his own net.
Paul Lambert's side had previously been one of the division's best defences but had no answer to Arsenal's incredible flurry.
Villa's preparations had been hampered by a virus hitting Lambert's squad and the Scot was forced into a late change when Ashley Westwood pulled out of the warm-up to join Nathan Baker as one of two players absent from the XI that had defeated Liverpool at Anfield.
|VIEW FROM VILLA PARK
|By Tom Davis
Aston Villa had built themselves on defensive solidarity this season. Three clean sheets and just one goal conceded had given them a sterner look at the back and, as noted by Paul Lambert in his programme notes before kick-off, it had given them momentum.
But that was crushed in four crazy first-half minutes as the league's best defence crumbled. A clinical Arsenal raced away with the three points.
Danny Welbeck and Mesut Ozil, whose partnership was a real bright point for Arsenal, combined for the first and second goals and both were taken superbly. Welbeck – now with four in three against Villa – is finally off the mark for his new club but Lambert's side will need to bounce back quickly from this deflating performance as fixtures against Chelsea, Manchester City and Everton in their next three games could prove sticky points after a fine season start.
It was Villa who appeared least affected by their enforced switch as they quickly claimed the initiative. Fabian Delph forced Wojciech Szczesny into a smart save early on with a fine effort from the edge of the area before Arsenal had to defend two corners to keep themselves level.
Welbeck wasted the visitors' most presentable opportunity of the opening exchanges, firing over from 25 yards with the Villa defence backpedalling.
Alan Hutton and Aaron Ramsey then traded harmless long-distance efforts but it was Ciaran Clark who failed to take a golden opportunity when he headed straight at Szczesny after meeting a curling free kick delivery from the left.
And Villa were left to rue that miss just past the half-hour mark, as Arsenal forged ahead in some style.
A fantastic Welbeck through-ball allowed Ozil to escape the hosts' defence for the first time in the match and he made no mistake in side-footing the ball past Brad Guzan.
Welbeck and Ozil then reversed roles, the German sliding a perfect pass across the box after being released on the left-hand side, which the forward gleefully smashed home.
Incredibly, Arsenal were not done there and Cissokho made it three goals in three minutes when he inadvertently turned home another low ball from out wide while attempting to clear.
The goals took the sting out of a previously buoyant home crowd, allowing Arsenal to cruise into the break 3-0 up and, though Lambert looked to turn the tide of the match at half-time by introducing youngster Jack Grealish in place of Andreas Weimann, Arsenal continued to control possession.
Chances were few and far between in the second period, with Villa looking to limit the damage and the visitors happy to hold onto a comfortable lead.
Arsenal did just that in the end, earning their first league win in over a month to move within three points of leaders Chelsea ahead of their clash with Manchester City on Sunday.