The poll showed that Truss "performed best" with 50% of the votes among the Conservatives, meanwhile 78% of voters think that the Foreign Secretary overall "did well" at the BBC debate on Monday.
Truss’ opponent, former Treasury Secretary Rishi Sunak, also did relatively well according to 65% of the voters. However, Conservative members decided that Truss outperformed Sunak on every single issue covered in the debate.
The new YouGov survey was conducted among 507 Conservative Party members on July 25-26.
Truss and Sunak are the two final candidates in the election race for the post of prime minister and head of the Conservative Party, following Boris Johnson's resignation on July 7.
The last round will take place by mail from August 4, with the winner determined by all party members, of whom there are about 200,000 to date. The results are expected to be announced on September 5, when Parliament resumes its work after the summer break.