Penny Mordaunt, a former Defence Secretary, came second with 67 votes. Third was Liz Truss, Foreign Secretary, securing 50 votes. Attorney General Suella Fernandes Braverman, who is of Goan Indian descent, scraped through with 32 votes.
A total of 358 MPs were eligible to vote.
Nadhim Zahawi, who briefly succeeded Sunak as Chancellor before Prime Minister Boris Johnson was forced to resign, and Jeremy Hunt, a Health Secretary and Foreign Secretary in previous governments, were eliminated. A candidate had to cross a threshold of 30 votes to remain in the race; which they failed to obtain.
The process involving directly elected Conservative lawmakers in the House of Commons is expected to by next week whittle down the competition to just two runners.
The voting will then be thrown open to all full members of the Conservative party – estimated to be around 160,000 – to express their preference.
A survey conducted by a leading polling company YouGov for The Times newspaper of the UK suggested Mordaunt would easily beat other candidates in the final ballot of the full membership. Her closest competition would come from Liz Truss, who, the pollster forecast, she would defeat by 55 per cent to 37 per cent votes.
If Sunak makes it to the last two, he is projected to lose by 67 per cent to 28 per cent votes.
Meanwhile, Johnson has thrown an extraordinary spanner in the works by tabling a confidence motion on his government on Monday.
If he loses the vote, there could theoretically be a mid-term general election, thus jettisoning the current leadership contest for his replacement.
If he wins, then, technically, it could raise the question as to whether his resignation last week is still valid.
The opposition Labour party had moved a motion in the House of Commons against Johnson so as to cut short his caretaker role. This was disallowed.
A government spokesman told media: “Labour were given the option to table a straightforward vote of no confidence in the government in keeping with convention. However, they chose not to. To remedy this we are tabling a motion which gives the house the opportunity to decide if it has confidence in the government.”
The Guardian quoted a Labour source as saying the proposal was “madness”, and added: “Not sure the Tory leadership candidates or marginal MPs will welcome this.”
–IANS