Rodrigues-Birkett narrowly took the lead after the 15-member Security Council voted a second time on Friday, according to diplomatic sources.
The 52-year-old UN ambassador, who has also served as Guyana's foreign minister, received eight votes in favour of her election, three against and four "without opinion."
She thus moves ahead of Costa Rica's Rebeca Grynspan, who took a narrow lead in the first informal vote in July.
The informal voting is expected to continue for several more rounds. A total of eight candidates are vying to replace António Guterres, who is stepping down at the end of the year.
