They made the decision even though they were advised by Mr Tierney that members could face legal action.
Residents had asked for the closure because of criminal activity on the laneway -- to the back of 183 to 211 Philipsburgh Avenue and 4 to 34 Annadale Crescent, Dublin 9.
Some 100 houses surround the route, where in the last year a garage has been burned down, two cars have been set alight and it has become a dumping ground.
Dublin North Central TD Finian McGrath said he and Cllr Damian O'Farrell are fully behind the closure, despite the city manager's warning.
"Locally, the laneway is called 'the laneway to hell'," he added.
"There was so much anti-social behaviour and so much intimidation and violence going on in it," Mr McGrath told the Herald today.
"We have been fighting to close that laneway for five or six years. Some residents had a number of near-misses, and by that I mean assaults that could have led to serious injury or death," the Independent TD said.
"I don't know what Eircom are going to do. I just know we are supporting the residents. Cllr O'Farrell put an awful lot of work into it," the said.
Mr Tierney had said Eircom was concerned about access and warned the council could be sued if the public right-of-way was extinguished.
However, a roll-call ballot of councillors came down in favour of closure by a massive majority of 36 votes to one.
Eircom was approached three times by the council as part of the consultation process in advance of the ballot.
However, on each occasion, the telecoms company objected. Eircom has plant equipment in the laneway and is concerned it might be damaged if the right of way blocked.
It is understood the company could sue if the equipment is in any way interfered with after the closure. Eircom had not replied to a request for a comment at the time of writing.