Ban is now almost certain to succeed Kofi Annan as he received 14 votes in favour in Monday's poll and one "no opinion", but more crucially no negative votes from any of the council's five members with veto-wielding power.
A candidate is required to receive at least nine positive votes and no veto.
An official poll is expected to be conducted on October 9 after which the 192 members of the UN General Assembly must approve the council's recommendation.
Shashi Tharoor, the runner-up in the official poll, announced the withdrawal of his candidacy after he received four fewer votes in favour than Ban and, more importantly, three against, one of which was a veto-holding member.
Tharoor, who is the current UN undersecretary-general for public information, gave his backing to Ban and told reporters he would "strongly support" Ban because "the United Nations and the world has a stake in his success".
In third place was Vaira Vike-Freiberga, the Latvian President, the only woman and non-Asian in the race, with five positive votes, two less than in the last straw poll.
Vike-Freiburga's tally was always likely to be academic after most council ambassadors agreed, at the insistence of China, that the next secretary-general should come from Asia because of a tradition that the post rotate among regions of the world.
Monday's crucial informal poll was the fourth held since July and the first to differentiate ballot sheets used by the council's 10 non-permanent members from those of the five veto-wielding permanent members.
The council's so-called "Big Five" used blue ballot sheets while their non-permanent counterparts cast white ones, according to diplomats.
Based on the results, John Bolton, the US Ambassador to the UN, said he urged the council to decide "as soon as possible, this week hopefully" when to schedule a formal vote on who will succeed Annan.