After a quiet start to the match the England man raced through before caressing the ball in to the far corner.
The visitors were level when Bacary Sagna fouled Gabriel Obertan 25 yards out and Demba Ba's resulting set-piece flew off Jack Wilshere's head in to the Arsenal goal.
Arsenal came out much stronger after the break, Kieran Gibbs drew a save from Tim Krul shortly before Alex Oxlade-Chamberlain beat the Dutchman to make it 2-1 with a fine low drive from 20 yards.
It was not long before Newcastle equalised. Gabriel Obertan turned Sagna inside out before his cross found the un-marked Sylvain Marveaux who tapped in to an empty net.
Arsenal were back ahead within five minutes when Fabricio Coloccini headed his clearance against the bar and the ball fell to Podolski who nodded home to make it 3-2.
And then Newcastle equalised again when Marveaux swung a ball to the back post where Ba turned it past Wojciech Szczesny.
Walcott then dug them out of trouble five minutes later when Gibbs slotted the ball across the box and he fired in to the roof of Krul's goal.
Oliver Giroud then killed off the game with five minutes left, latching on to Walcott's cross to head between Krul's legs and the Frenchman then rubbed salt in to Newcastle's wounds by slotting home to make it 6-3.
Walcott then got the hat-trick he deserved in injury time, picking himself off the turf after being flattened before chipping the ball over Krul with a brilliant finish.