The phrase "narrow victory" means winning by a very small margin or a close win, often just barely beating the opponent or competition. Full definition
Bronx District 13 (Pelham Bay and the Northeast Bronx): The race to succeed term - limited James Vacca saw Assemblyman Mark Gjonaj win a surprisingly narrow victory over progressive activist Marjorie Velazquez even though Gjonaj spent over $ 700,000, more than any other Council candidate. (shakingnews.com)
President Trump won the Electoral College with narrow victories in three states, despite having lost the popular vote to Hillary Clinton. (ecommercetimes.com)
The 2000 referendum on whether to approve an amendment to the District's charter that would change the size and method of selecting the board of education provided a very narrow victory for the mayor's proposal. (educationnext.org)