In the prior Journal/NBC News poll, conducted in mid-July, Mr. Carson had only 10% support, compared with 19% for Mr. Trump. The retired neurosurgeon overtakes Mr. Trump in the new survey, conducted Sept. 20-24, when voters’ first choice is combined with their second.

No candidate in the race has enjoyed a swifter ascent than Mrs. Fiorina, who barely registered in the July survey. She has since taken the spotlight in the GOP race after a strong performance in a televised Sept. 16 candidate debate.

Some 28% of Republican primary voters picked her as their first or second choice in the September survey, up from 2% in the July poll.

By contrast, former Florida Gov. Jeb Bush lost the most altitude since the prior Journal/NBC News survey.

Some 7% of Republican primary voters named Mr. Bush as their top pick for the GOP nomination, down from 14% in July and 22% in June.