Picking up where he left off against Chelsea, Walcott put Basel to the sword with two first-half goals amid one of his finest Arsenal displays.
The 27-year-old raced into the box to head home Alexis’ cross, and he added a second with a low drive after a slick one-two with Alexis.
Basel keeper, Tomas Vaclik, kept the score down with fine saves from Hector Bellerin, Alexis and Nacho Monreal, while Mesut Ozil could have had a couple himself.
The score could have been anything at half-time and, although the tempo dropped after the break, this was still an emphatic Arsenal victory.
The Gunners go joint-top of Group A with Paris Saint-Germain with four points from two games.
In other Champion League games Ludogorets Razgrad lost 1 – 3 to Paris Saint Germain. Both teams are in Group A with Arsenal and Basel.
In Group B, Basiktas and Dynamo Kyiv game ended 1-1 while SSC Napoli and Benfica game ended 4-2 in favour of SSC Napoli.
Borussia Moenchengladbach and Barcelona game in Group C ended 1-2 in favour of the Spanish club while Celtic and Man City game ended 3-3.
In Group D, Atletico Madrid defeated Bayern Munich 1 – 0 in a Champion’s league cracker while the game between FC Rostov and PSV Eindhoven ended 2 – 2.
In Group E CSKA Moscow was beaten at home by Tottenham Hotspur 0 – 1 while Monaco drew 1-1 with Bayer Leverkusen.