It was 3-0 within 25 minutes as Holding got his first Arsenal goal, turning into the net from close range after Walcott's corner was glanced on by Per Mertesacker. Arsene Wenger's men are now at the top of Group H on six points.
Theo Walcott opened scoring for Arsenal on nine minutes before adding a second in the 22nd minute to make it 2-0. His header was saved initially but Walcott was able to get to the rebound and put Arsenal in front. BATE's goalkeeper, Denis Scherbitski, passed the ball straight to Walcott who couldn't believe his luck and scored easily to double Arsenal's lead.
Rob Holding almost had his second goal for Arsenal from another corner but he swung at the ball and smashed his shot off the post.
However, the visitors were gifted a goal in the 22nd minute when Scherbitski passed the ball straight to Walcott - who fired it past him again.
Nonetheless for the neutral Arsenal's early goals rather diluted the spectacle as a serious contest and even when Mirko Ivanic pulled one back for the Belarusians on the half-hour mark one sensed a comeback was never on the cards.
Ospina could not stop Ivanic's effort.
Scherbitiski made amends on one particular occasion to tip away another Walcott effort away at full-stretch to temporarily deny his hat-trick. It was a typical Arsenal goal - Wilshere and Olivier Giroud combined on a 1-2 to get Jack to the byline, and he chipped a ideal ball back across the face for Theo.
With Lyon drawing against Atalanta in the other pool tie, the Toffees are bottom of Group E after two games and manager Ronald Koeman couldn't hide his frustration with his players.
Gordeychuk made it 4 - 2.
Arsenal youngster was handed a debut in Belarus.
Indeed, the last newly promoted side to win at the Emirates in the Premier League were Newcastle in November 2010 - then managed by current Brighton boss Chris Hughton. Walcott was causing the hosts problems with his pace and it was only a matter of time before Arsenal broke the deadlock.