The opener came in the 7th minute when Alexis Sanchez made a clever run off the shoulder of the defender to race onto a ball from Santi Cazorla before chipping a lovely left-footer onto the head of Walcott who put it away for just his second headed goal for Arsenal.
Less than 20 minutes later and the Gunners had doubled their advantage when Walcott played a neat one-two with Sanchez who flicked the ball back into the path of the Englishman who needed no second invitation to fire across goal, nestling the ball inside Tomas Vaclik's far post.
The Basel keeper had a busy first 45 minutes to continually deny the Arsenal attack, keeping out clear chances from Sanchez and Hector Bellerin, while strongly defending a number of half opportunities.
Arsenal's brilliant one-touch passing continued in the second half and despite David Ospina having to tip Birkir Bjarnason's curling effort over the bar just after the hour-mark, they had little to worry about as Basel attempted to stem the bleeding.
It was academic as the second half ticked on and both sides appeared to put the cue in the rack in what was a much less exciting affair, apart from late on when there was some end to end action.
Vaclik again came up with a top quality save to deny Sanchez at the back post in the final minute of regular time but the damage had already been done as the Gunners set themselves up for another Round of 16 berth.
2016/17 UEFA Champions League - Group A