The final draft of the resolution hammered out after a day's delay by non-permanent members Indonesia and Germany was passed unanimously on Tuesday in its barebones form extending the mission of the UN Assistance Mission in Afghanistan (UNAMA).
It is a political and aid mission without a peacekeeping component in the country where the US and nominally the NATO have stationed about 14,000 troops.
This is the second time in recent months that China has had to publicly back down in the face of opposition from other members.
While previous resolutions on the UNAMA mandate had language promoting efforts like the OBOR to help Afghanistan's trade and transportation, the US had insisted that the references be dropped this time and China had threatened a veto if the measure did not include its project.
China and the US have veto powers as permanent members.
Some other members of the Council also joined the US in opposing the OBOR reference, while Russia reportedly backed China.
It withdrew its opposition to Pakistan-based Jaish-e-Mohammed chief Maulana Masood Azhar being designated a global terrorist.
Newly-appointed US Permanent Representative Kelly Craft accused China of putting its own interests ahead of those of Afghanistan.
Beijing's insistence "on language that highlights national political priorities rather than ways in which we can most effectively assist the people and the government of Afghanistan" had weakened UNAMA's mandate.
China's Permanent Representative Zhang Jun countered by accusing a "few countries" of going back on the previously agreed consensus resolution draft.
The strong US position on OBOR reflects its unease with the growing economic influence of China and Beijing's ambition to build a trade zone outflanking the West.
Washington has been negotiating with the Taliban on a peace deal that would enable US President Donald Trump to keep his election promise of bringing US troops home from there.
However, Trump put the negotiations on hold after the Taliban killed a US service member.
(Arul Louis can be contacted at arul.l@.in and followed on Twitter @arulouis)
( With inputs from IANS )