Webster, who had already beaten Newton but lost to Simon Whitlock prior to a decisive evening on Monday, claimed a 5-3 win against Ross Smith to boost his chances of qualification in his final Group G match.
But Newton’s 5-4 win against Whitlock left them at deadlock, setting up the shoot-out which the Welshman won convincingly.
Webster won the bulleseye and opted to throw second. It proved a shrewd decision as Newton only managed to score 40 with his first three darts.
‘Spider’ took control by firing in 135 before the world number eight took a narrow lead with a ton.
Webster the scored 137 to increase his total to 272 and that proved to be more the enough as ‘The Warrior’ failed to overtake him with his 59.
The left-hander will face Scott Waites in the last 16 in a battle of former Lakeside champions.