Allcock, 14-5 up against Zambia's Duncan Naysmith, saw his lead gradually whittled away as his opponent came back to lead 23-22 after 30 ends. However, Allcock hit back with a single and a double for a 25-23 victory.
Corsie had an even bigger scare against Argentina's Jose Riveros, who led 24-20 after 32 ends, but the Scot finished with four shots in four ends to squeeze home, 25-24. 'I won't get things any harder than that. It was really tight, and I'm very relieved to have survived,' he said.
The unbeaten Jeff Rabkin from Israel trounced the Commonwealth gold medallist, Rob Parrella, from Australia 25-8. New Zealand's Peter Belliss scored his eighth straight victory when he beat Swaziland's Hayley Abrahams 25-13, but Zambia's Duncan Naysmith had his winning run halted by Guernsey's Mike Smith, who triumphed 25-21. Will Thomas from Wales beat Barry Wilson from the Norfolk Islands 25-7, and Ireland's Stevie Adamson defeated Rudy Wild from Papua New Guinea, 25-16.
In the fours, Scotland's team of Graham Robertson, Angus Blair, Willie Wood and Alex Marshall moved to the top of their section when they surged to a 27-12 win over the previously unbeaten Israeli rink.
The Englishmen, John Ottaway, Roy Cutts, Andy Thomson and John Bell, survived a scare before collecting their eighth straight win. They trailed Fiji 16-11 with just seven ends to play, but recovered to snatch a 20-18 victory.
They then received more good news from the jury of appeal, who considered Andy Thomson's use of unregistered bowls during Wednesday's win against Japan.
The jury were happy that there had not been any infringement of the laws of the game, although there had been a breach of tournament rules, for which the England team manager, Mal Hughes, was severely reprimanded.