At a hustings meeting at Westminster attended by 45 Tory MPs, allies of David Davis abandoned their plan to question Mr Cameron about whether he had ever used a class-A drug.
Amid claims of "dirty tricks", Mr Cameron, the 39-year-old shadow Education Secretary, emerged unscathed from a 25-minute grilling by the right-wing 92 Group.
Mr Cameron's campaign gained further momentum when he won the support of Theresa May, the former Tory chairman and a leading moderniser, and two right-wingers, Bernard Jenkin and Douglas Carswell.
Mr Cameron has faced questions from the media about whether he smoked cannabis while a student. On Sunday, he refused to answer but said he " did a lot of things before I came into politics that I shouldn't have done".
At the hustings meeting, there were clear signs his rivals were planning to exploit the issue when the four candidates took questions separately. In the first session, Mark Pritchard, MP for The Wrekin and a David Davis supporter, asked Ken Clarke, the former chancellor, whether he had ever used a class-A drug.
Mr Clarke made clear he did not believe such personal questions should be an issue in the election but added "for the record" he had never used cocaine.
With the Cameron camp sensing a "stitch-up," Mr Pritchard was persuaded by a fellow Davis supporter during a break in the meeting not to ask Mr Cameron the same question. When he took his turn before the MPs, Mr Cameron was asked a much broader question about drugs policy but not whether he had used hard drugs.
Mr Cameron, who backed the Government's decision to downgrade cannabis from a class-B to class-C drug in the last parliament, hinted he was having second thoughts by saying stronger forms of cannabis were now widely available. He said that the decision should be reviewed in the light of the latest scientific evidence. Mr Cameron may yet face further questions about whether he has taken certain drugs. His aides say that he will stick to his line and not be more specific. The Cameron team is increasingly confident he will win a place on the shortlist of two to be chosen by Tory MPs a week today, which then goes to a ballot of the party's 300,000 members. There is growing speculation among Tory MPs that he will face Mr Davis in the shoot-out, with Liam Fox, the shadow Health Secretary, and Mr Clarke being eliminated in two rounds of voting at Westminster next week.
Mr Clarke sought to reassure the Eurosceptic-dominated 92 Group that he would not split the party over Europe. He received a boost when he won the backing of John Penrose, the first newly elected MP to support him.
Today Mr Davis will woo Tory right-wingers by proposing education vouchers one of the items on the 92 Group's shopping list of policies. In a speech, he will say vouchers would transform opportunities in the inner cities.
Mr Jenkin, who managed Iain Duncan Smith's winning campaign in the 2001 leadership election, said he was backing Mr Cameron because he had "the courage, integrity and the intellect to give our party the best opportunity of forming a successful Conservative government".
Dr Fox is optimistic of winning support of about 15 MPs from the Cornerstone Group, which could take his tally of supporters to between 25 and 30.