Baki began her political career as Ecuador's consul to Beirut in 1981. From 1992 to 1998, she was an honorary consul in Boston, Massachusetts in the United States of America.[4]
In 1995, Baki and Roger Fisher received a request from the President Sixto Durán Ballén to participate in the peace deliberations of the Cenepa War between Ecuador and Peru. Both accepted and agreed to cooperate, moving to Ecuador and were involved in the process that led to the Brasilia Presidential Act in 1998.[5] In the same year, Jamil Mahuad, the new president of Ecuador, appointed Baki the Ecuadorian Ambassador to the United States of America,[6] the first woman appointed to this office.[5] In this position, Baki played a key role in achieving favorable trade agreements with the United States.[6]
In 2000, Baki founded the Galapagos Conservancy Foundation,[7] after an oil spill took place in the Galapagos Islands, with the aid of American tycoon Donald Trump, whom she had met and befriended during a diplomatic trip to the United States.[8] During the 2002 Ecuadorian general election, Baki made a failed attempt for the Presidency of Ecuador as head of META.[9]
On 15 January 2003, Baki was appointed Minister of Industries and Productivity [es] by President Lucio Gutiérrez, yet again becoming the first woman to occupy that office.[10] While holding this office, Baki also managed to have Miss Universe 2004 hosted in Quito, Ecuador thanks to her friendship to Donald Trump, owner of the company that organized the event. In response to criticism levied at her over the high cost of the event, Baki said that the money was "an investment" and not an expense and that it would provide an "excellent opportunity to promote the country [Ecuador] abroad."[11] Another landmark of Baki's running of the Ministry was her attempt to establish a Free Trade Agreement with the United States, which was widely criticized by indigenous groups, who held demonstrations against Baki's ministry.[6]
During the 2006 legislative election [es], Baki was elected to the Andean Parliament to represent the Patriotic Society Party.[12] Once her membership of the Andean Parliament began, the Ecuadorian delegation proposed as a candidate for the Presidency of the Parliament for the 2007–2009 term.[5]
At the beginning of 2010, she was elected head of the team negotiating Yasuní-ITT Initiative by President Rafael Correa with the objective of raising 3,600 million dollars from the international community in exchange for the cessation of exploiting of approximately 846 million barrels of oil underneath Yasuni National Park.[13] The project could not achieve these goals and was dissolved mid-2013.[14]
In February 2020, Baki was confirmed as Ambassador to the United States by President Lenín Moreno.[2] In February 2024 she became Ecuador's ambassador in Paris but that appointment was terminated on 6 November 2024 by President Noboa.[15]