The YouGov poll for The Times newspaper showed 60% support for the foreign secretary versus 26% for Sunak, with the remainder undecided. It was conducted over the past five days.
It comes as a huge boost for Truss on arguably the worst day for her campaign, as she was forced to backtrack on a flagship policy to slash £8.8 billion from public sector pay outside London.
Truss has built on her lead in a previous YouGove survey, published on July 21, which put her ahead of the former chancellor by 24 points.
Truss scrapped the plan to pay workers in cheaper regions less than their counterparts in the capital and the south east on Tuesday morning, a little over 12 hours after making the major announcement.
The foreign secretary insisted her policy had been “misrepresented”, and argued people had been “unnecessarily worried” about cuts as she confirmed she would not be going ahead with the regional pay boards.
It was unclear how the Truss camp believed the policy had been misconstrued, with a news release clearly stating that up to £8.8 billion could be saved by extending the move for all public sector workers.
Former chief whip Mark Harper told Truss to stop “blaming journalists – reporting what a press release says isn’t ‘wilful misrepresentation’”.
The first major gaffe from Truss’s campaign came as Sunak battles to make up ground during what is a crunch moment in the contest, with ballot papers going out this week.
Monday night’s hustings will be followed by three further head-to-head clashes, including a televised Sky debate on Thursday.
The Sunak campaign had hoped that his pledge to cut income tax would boost his chances as Tory Party members receive their postal votes.
But the YouGov poll indicates Truss is set for a victory as comfortable as that of Boris Johnson over Jeremy Hunt in 2019. And suggesting Sunak was the smallest window to claw back the deficit, 45 per cent of members questioned by YouGove saying they would vote as soon as they received their ballot paper this week.