The Foreign Secretary won a 34-percentage point lead over Mr Sunak in a YouGov poll of party members, before a survey for the ConservativeHome website put her 32 points ahead.
Mr Javid, whose resignation as health secretary minutes triggered a cascade of resignations forcing Boris Johnson to quit as Tory leader, threw his support behind Ms Truss.
He claimed that “tax cuts now are essential,” while Mr Sunak has said tackling inflation is needed before tax cuts.
A former chancellor, Mr Javid also warned in an article for the Times that the nation risks “sleepwalking into a big-state, high-tax, low-growth, social democratic model which risks us becoming a middle-income economy by the 2030s”.
“If we can renew our government with a bold agenda, the Conservatives can still beat Labour, the Lib Dems and the SNP at the next election – and the evidence suggests Liz is the best-placed candidate to do so,” he added.
His backing of Ms Truss came shortly before the latest hustings of Tory members at an event in Cardiff on Wednesday evening.
The YouGov survey showed 60% of the party members polled between July 29 and August 2 said they intend to vote for the Foreign Secretary, with just 26% backing Mr Sunak.
The poll of 1,043 Conservative Party members indicates just 11% do not know who they will vote for, while 2% said they will not take part in the contest.
A further indication of Ms Truss’s commanding lead came with a survey of 1,003 members by the ConservativeHome website, which had 58% backing her to Mr Sunak’s 26%.
The Truss campaign said in a statement that the former Health Secretary’s endorsement was a sign she was uniting the party.
“His support signals that Liz is bringing the party together and they’re uniting behind her bold plan to cut taxes, grow the economy and deliver for the country,” said a spokesperson.
However, her campaign has suffered some setbacks in recent days after she abandoned a pledge to cut the public sector wage bill by paying workers in cheaper areas of the country less than in more expensive parts – claiming it had been “misrepresented”.
Critics of the plan had claimed it would go against the Government’s levelling up agenda by cutting wages in more deprived areas of the country, although Ms Truss insisted it was never meant to impact people’s current pay rates.
Under questioning during a leadership hustings of Tory members in Cardiff, Ms Truss insisted the plan was never intended to apply to doctors, nurses and teachers.
Asked who had got the policy wrong, she said: “The media.”
Mr Sunak welcomed her U-turn, saying it would have meant “almost half a million workers in Wales getting a pay cut”.
The Foreign Secretary renewed her attacks on Scottish First Minister Nicola Sturgeon during the hustings after labelling her demands for an independence referendum as attention seeking.
She went on to criticise Wales’s Mark Drakeford as a “low-energy version of Jeremy Corbyn”, and called Labour’s Sir Keir Starmer a “plastic patriot”.
The first postal votes in the contest were due to be submitted this week, but the party delayed sending ballots out following advice from cyber security experts.
The party has made changes to its process on the advice of the National Cyber Security Centre (NCSC), part of GCHQ, following warnings that hackers could change members’ votes.
The ballots had been due to be sent out from Monday but could now arrive as late as Thursday August 11.