Sanchez got the first with a masterful chip from just inside the box.
Walcott powered a curling shot home after Ludogorets’ Wanderson hit a post.
Alex Oxlade-Chamberlain smashed a loose ball into the corner for the third, before Ozil scored three times in a game for the first time in his career.
The Gunners have now won seven games in a row in all competitions – scoring 23 goals – and are undefeated in 11 matches.
Their last defeat was at home to Liverpool on the opening day of the Premier League season.
Victory over Bulgarian champions Ludogorets means Arsenal top Group A ahead of Paris St-Germain, who beat Basel 3-0, on goal difference.