If the ball goes near your goal, get rid!
The home side burst into life after 20 minutes when Giroud lost possession and Mirko Ivanic shot narrowly wide from outside the box when a cross was half cleared.
They were already 2-0 up by then with their second goal on the stroke of halftime from forward Allan Saint-Maximin, who picked off a stray pass in his own half and burst downfield to score.
A nervy finish stretched Arsenal at the back, but their brilliant opening blitz had secured victory.
It didn't take long for Wilshere to show off his pedigree in this Europa League fixture. We all know that Wilshere has awful luck with injuries, and that he is often his worst enemy in terms of behaving himself off the pitch. All told, a youth-filled Arsenal side won three points on the road. Like Wilshere, consistency is the key for him.
Even then, owing partly to their inexperience and Wilshere's advanced role when he could have offered direction from central midfield, Arsenal's lack of shape gave their hosts further opportunities. Subs: McGuane 7, Nketiah 6.
Arsenal's Per Mertesacker and Shkodran Mustafi in action with BATE Borisov's Mikalay Signevich.
They should have made it 4-3 only for Aliaksandr Volodko, unmarked near the penalty spot, to blaze a first-time effort over the top.
Walcott was gifted his second when Shcharbitski, in an attempt to play out from the back, kicked the ball straight to him.
25' - GOAL! BATE 0-3 Arsenal.
Zenit St Petersburg won the big game in Group L against Real Sociedad and opened up a three-point lead at the top of the table with a 3-1 victory in Russian Federation.
Everton rallied to 2-1 ahead and looked set to rebound from its previous 3-0 loss to Atalanta.