The former Cabinet minister received 114 votes in the first round of a secret ballot of Tory MPs held in the House of Commons, followed by United Kingdom foreign secretary Jeremy Hunt in second place with 43 and environment secretary Michael Gove third with 37 votes.
Theresa May is set to become Britain's next Prime Minister after her internal party Andrea Leadsom dropped out of the Conservative leadership race.
May will now go head to head with Leadsom in an all-woman contest.
Britain's ruling Conservative party on Tuesday began the first round of voting to choose a new party leader who will succeed David Cameron as the prime minister with home secretary Theresa May emerging as a clear front-runner.
May was the clear frontrunner in the race and bagged 165 votes in the first round, which resulted in the first elimination of a candidate with the least votes.
The 42-year-old British Indian MP for Richmond in Yorkshire maintains his lead in the race to replace Boris Johnson as nominations formally opened for the contest.
An "emotional" British Prime Minister David Cameron on Tuesday chaired his last cabinet meeting before handing over the baton to Theresa May who will assume charge on Wednesday, becoming the United Kingdom's second woman premier after Margaret Thatcher.
In a cabinet that was already being touted as the most diverse in British history, Priti Patel became the first Indian-origin home secretary with Pakistani-origin Sajid Javid moving from the UK Home Office to become the new chancellor.
UK environment secretary Michael Gove became the latest Tory MP to announce his intention to challenge Johnson on Sunday.
The 47-year-old senior cabinet minister was widely expected to become the third female British Prime Minister after 170,000 online and postal votes cast by Tory members, ending Sunak's historic run as the first member of Parliament of Indian heritage to compete for the top job at 10 Downing Street.
The PM said the new line-up brought in "talent from across the whole of the Conservative party".
Gove, who had surprised political circles with his decision to stand for the Conservative party leadership instead of backing fellow Brexit champion Boris Johnson, laid out his case to be premier despite not being glamorous enough.
Theresa May on Wednesday became Britain's second woman prime minister after Margaret Thatcher.
Apart from May, the four other contenders for the Conservative leadership and prime ministership are Stephen Crabb, Liam Fox, Michael Gove and Andrea Leadsom.
She stepped down after failing to win over her ministers with a revised strategy over her plans for the UK's withdrawal from the European Union.