With just three candidates left in the race triggered by David Cameron's resignation, Michael Gove, a prominent "Leave" campaigners was knocked out after polling just 46 votes.
"People need certainty and they will get it", she said.
"I think the country requires fresh leadership to take it in this direction", Cameron said upon resigning.
Theresa May will face Andrea Leadsom in the final round of voting to become the new Conservative Party leader and Prime Minister.
The final election will take place on September 9, when 150,000 members of the Conservative Party are expected to choose the first female prime minister since Margaret Thatcher.
Mr Duncan Smith, who is supporting Mrs Leadsom's bid, said he was pleased that "two strong women" would now battle to become the country's second female prime minister.
Head of Sky Data Harry Carr said: "After six years as Home Secretary, Theresa May is undoubtedly benefiting from the higher profile she enjoys among the wider public".
You may remember: he first backed Boris Johnson's bid to be Prime Minister, then stabbed Boris in the back and ran himself.
However, the decision was opposed by Cameron resulting in his announcement to step down immediately after the party elects a successor.
The victor will replace Prime Minister David Cameron, who announced his resignation after Britain voted last month to leave the European Union. The victor will become the second woman prime minister in Britain after Margaret Thatcher. The victor will become the country's second female prime minister.
Speaking on the BBC's Andrew Marr Show on Sunday, Ms Leadsom was asked if, as leader, he would include Mr Farage in exit negotiations.
Mrs Leadsom's departmental boss, Energy Secretary Amber Rudd, is backing Mrs May and took aim at her junior ministerial colleague's lack of government experience.
On Tuesday Mrs May was the most popular candidate in the first round of voting, picking up 165 votes of a possible 329.
May supported Britain remaining in the European Union, but has pledged to hold up the Brexit vote.
May, who supported Britain's continued membership in the European Union but did not campaign prominently for the "Remain" side in the referendum, has stressed her experience as a senior Cabinet member.
Although Theresa May won the majority of votes by Conservative MPs, Andrea Leadsom is gaining in popularity among the party rank and file.
She paid tribute to Mrs Leadsom's "guts" in putting her name forward for leader, and said she hoped the leadership contest would see a "big, broad debate" being held across the country.