SAN FRANCISCO — By last Friday afternoon, most of Uber’s eight directors had gathered in San Francisco for a board meeting. Their agenda was simple: Pick a new chief executive for the ride-hailing company.

What unfolded over the next 72 hours was anything but straightforward.

In discussions at the Four Seasons Hotel downtown and at the offices of the private equity firm TPG Capital, which holds an Uber board seat, directors operated under the cloak of secrecy. They spoke in a kind of code about some of the candidates, limiting knowledge of the shortlist to a handful of people.

By Sunday morning, one of the finalists, the former General Electric chief Jeffrey R. Immelt, had publicly pulled out. Some board members were behind another finalist, Meg Whitman, chief of Hewlett Packard Enterprise, and some people close to the process had taken steps to prepare for an announcement of her appointment.

But as Sunday wore on, Ms. Whitman, emboldened by her front-runner status, started negotiating for increasing control over Uber were she to accept the job, siding with one faction of the board that wanted to limit the clout of Travis Kalanick, the former chief. Those tactics deterred most board members, who then swung decisively in favor of Dara Khosrowshahi, the chief executive officer of Expedia.