Unai Emery's side were humbled away at Rennes on Thursday, but rallied to see off Ole Gunnar Solskjaer's side and inflict the interim manager's first Premier League defeat.
Nemanja Matic and Paul Pogba returned to the United lineup after missing the famous comeback against Paris Saint-Germain on Wednesday, with Anthony Martial fit enough for the bench.
Unai Emery and Arsenal opted for a very attacking lineup, with Pierre-Emerick Aubameyang, Alexandre Lacazette, Mesut Ozil and Aaron Ramsey all starting.
The first-half was pretty even, with Xhaka scoring the opening goal courtesy of a swerving effort that totally deceived David de Gea in the United goal.
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Gary Neville was quick to criticise the Red Devils goalkeeper in commentary, but the windy conditions and late swerve on the ball made it incredibly difficult for De Gea.
United had their chances to equalise before the break, with Bernd Leno pulling off a brilliant save to thwart Lukaku.
The German goalkeeper also denied the Belgian in superb style after the break, as Arsenal recklessly broke forward in search of a second goal.
But just before the 70 minute mark, the Gunners were awarded a rather dubious penalty after Fred was judged to have brought down Lacazette in the area.
Aubameyang then stepped up and made amends for his miss against Tottenham last weekend, cooly slotting the ball past De Gea.
The Gunners were then able to keep a rare clean sheet under Emery to leapfrog the Red Devils in the table.
With Tottenham losing to Southampton and Chelsea only managing a 1-1 draw with Wolves, Arsenal are looking very strong contenders to finish in the top four.