Just 24 hours after the pair made it through to the final run-off in the Conservative leadership contest, the YouGov poll gives the foreign secretary a 24-point lead over the former chancellor.
The research – conducted after the final MPs’ ballot on Wednesday – shows that 62 per cent of party members intend to vote for Ms Truss, compared to 38 per cent for Mr Sunak.
The pollster’s previous survey earlier this week gave Ms Truss, who has pledged to introduce multi-billion pound tax cuts from “day one”, including reversing a planned hike in corporation tax, a 20-point lead among members.
YouGov added in its most recent poll of 730 members that the foreign secretary, who has the backing of some of Mr Johnson’s closest allies, “holds sizeable advantages over Rishi Sunak on key metrics such as trustworthiness and ability to lead the party”.
While just 18 per cent of Tory members said Ms Truss cannot be trusted to tell the truth – compared to 63 per cent who said she could – 40 per cent said Mr Sunak could not.
It comes as the pair begin the arduous task of competing to win over the support of members in hustings across the country over the summer, before the new Tory leader and the UK’s next prime minister is announced on 5 September.
In her first campaign visit since winning a spot in the final two, Ms Truss took a swipe at her rival and said it would be “very hard for Conservatives to win an election” if there is no change to the current economic policy.
Asked if Mr Sunak could win an election as a Tory prime minister, she told broadcasters: “I think the problem is that if we continue with our current economic policy, which is forecast to lead to a recession, it will be very hard for the Conservatives to win an election.
“I’m somebody who pushes through, gets things sorted out and gets things done. That’s why I want to be prime minister. This is a critical time for our country. We need bold action.
“We are in economic difficulty, the whole world is in economic difficulty. It’s not time for business as usual.”
In the fifth and final ballot of MPs – the process that whittled down the contenders to just two to face the membership – Mr Sunak emerged as Tory MPs’ choice, scooping 137 votes – 38 per cent of the parliamentary party.
Ms Truss won the support of 113 (32 per cent), after gaining the backing of the 59 supporters of fellow right-winger Kemi Badenoch, who was eliminated in the previous round.