49-year-old Abbi, a first-time councillor from Mukherjee Nagar ward, got 170 votes while Sharma secured 82 votes in the election held at a special meeting of the Municipal Corporation of Delhi. Eight votes were invalid.
The election of Mayor witnessed some stormy scenes earlier with Congress members objecting to Abbi's candidature alleging that she was holding an office of profit as she was a Delhi University professor.
BJP members claimed that she had taken permission from the DU before contesting the MCD elections.The new Mayor, who replaced incumbent Prithvi Raj Sawhney, has become the second woman in the post in BJP's five-year term in the corporation. Arti Mehra was the Mayor of Delhi for two years in succession from 2007.
The BJP had earlier witnessed a brief rebellion in its ranks as councillor Narain Singh had also filed his nomination for the post of Mayor, but was persuaded to withdraw.
Abbi is an associate professor in the faculty of law in the DU. She is also an alumnus of the same university. She is a specialist in commercial and consumer laws and had been a topper in LLB and LLM exams.
She had earlier said if elected, her priorities will be to work on a mission mode to ensure a clean Delhi, improve the image of the MCD and strongly oppose its proposed division into five parts.