Defender Hector Yuste netted with just two minutes to go to stun the Toffees and goalscorer Wayne Rooney said: "The goals were sloppy".
Despite an at times ragged second-half display however, Arséne Wenger's men eased home, with striker Olivier Giroud adding a fourth from the penalty spot to become the 19th player to reach a century for The Gunners in the club's history.
Following up on his victor against Doncaster, Theo Walcott did well to take the chances that were given to him which put Arsenal in control of the game very early on.
An error from BATE goalkeeper Denis Shcherbitski handed Walcott his second, capitalising on a woeful clearance before drilling into the bottom left corner from 12 yards.
Theo Walcott scored the opening two goals in the ninth and 22nd minute. Mirko Ivanic ran unmarked into the box and thundered a header past David Ospina who could do nothing but watch the ball fly by.
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Walcott was inches from a hat-trick before the break, forcing Shcherbitski into a superb fingertip save, before Holding hit the post from the resulting corner as BATE struggled to deal with Arsenal's set pieces.
Three minutes into the second half, Arsenal restored their three-goal lead.
However, Astana hung in there and equalised two minutes before half-time through Marin Tomasov's low shot from inside the penalty area. Then Ospina saved Ivanic's header but palmed it straight into the path of Mikhail Gordeichuk who thumped home from close range. It finished 4-2 but could've easily been about 8-5.
Nemanja Milunovic - 4/10 - Similarly to Hayduchyk next to him, he found it extremely hard to deal with Arsenal's link up and mainly found himself hoping Arsenal would miss in front of goal.
The Belarusian side are no slouches and they've beaten the likes of Athletic Bilbao, Bayern Munich and Roma in recent seasons, but for the most part the Gunners were utterly dominant. Walcott was causing the hosts problems with his pace and it was only a matter of time before Arsenal broke the deadlock.
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All this is to say that if Japan has its economic and commercial interests in India, it has similar interests in Pakistan as well. What have you (Pakistan) produced? "Pakistan's Prime Minister spoke of a "Comprehensive Dialogue" between our two countries.
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The company said that in 2015 it invested 800 million Canadian dollars ($656 million U.S.) in the plant to build the new Equinox. Though a small number are made in Mexico, the vast majority are built at CAMI plant and is the only model the plant now builds.