The National Railway Museum's proposals for a new central hall have been approved after a knife-edge vote.
Under plans, the two halves of the museum will be united with a rotunda.
The scheme has attracted significant opposition as it will see Leeman Road cut off, with a 437-yard (400m) diversion in place instead.
Holgate ward councillor Rachel Melly said: "This decision is a huge blow for local residents."
The application was deferred at a meeting last month for an equalities impact assessment to be carried out after some councillors raised concerns about the impact on disabled people.
The plans were discussed for hours on Friday at a fresh meeting, before ten councillors voted, according to the Local Democracy Reporting Service.
Five were against the plans while the other five were for them.
Planning committee chair, Chris Cullwick, used his deciding vote to push ahead with the application.
Residents will only be able to get through the museum during opening hours, and will have to queue at busy times, with the possibility of bags being searched.
An alternative route around the museum has to be in place before Leeman Road is closed.
Paul Clarke, a director of the St Peter's Quarter Residents' Association, said: "The applicant has ignored the views of local residents at every turn - putting their own commercial interests first."
National Railway Museum director Judith McNicol said the museum took "issues surrounding access and equality very seriously" and explained that they had employed accessibility consultants when designing the building.
Planning consultant Janet O'Neill said: "You can never make everybody happy. There's a clash between what the residents and what the museum wants… to say no stone's been left unturned isn't an exaggeration."