The Germany international has faced scrutiny in recent weeks after enduring a mixed start to his second season at the Emirates Stadium, but he helped the visitors put the disappointment of a midweek UEFA Champions League defeat to Borussia Dortmund behind them with an outstanding performance at Villa Park.
Ozil opened the scoring with a calm finish inside the box before teeing up Danny Welbeck to open his Arsenal account two minutes later.
And Aly Cissokho's own goal completed an incredible three-minute scoring spree, which Arsenal built on with a controlled second-half performance that saw them ease to three Premier League points.
Villa's preparations had been hampered by a virus hitting Paul 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.
Arsenal were also required to change their team before kick-off, with Alex Oxlade-Chamberlain starting and Alexis Sanchez named on the bench.
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 throughball 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 Welbeck 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.
