On the key campaign issue of tackling the country's cost-of-living crisis, Sunak renewed another previous assertion that he would "rather lose" than "say things that can't be delivered".
The survey also shows a majority in favour of ousted leader Boris Johnson, with 55 per cent saying that Tory MPs were wrong to effectively force him to resign and 40 per cent saying they were right.
The main reason mentioned by people who backed Truss was dislike of Sunak. Some 2 per cent of Tory members cited race or ethnicity as a reason for supporting Truss and not Sunak.
After the two contenders put forward their arguments for why they should replace Johnson, the audience members were asked who they thought had won the argument and they picked Sunak.
An estimated 180,000 party members started receiving their ballot papers this week and have the option of a postal or online ballot, which must be registered by the evening of September 2.
Rishi Sunak, 42, was an early backer of Brexit and took over as chancellor of the exchequer in February 2020. It was a baptism of fire for the Tory rising star, as the Covid pandemic erupted.
The former finance minister's pledge comes after his rival in the final two of the race to lead the ruling Conservative party, Liz Truss, accused him of being weak on China and Russia.