Stephen Colbert can finally claim complete bragging rights.

For the first time, Mr. Colbert’s “Late Show” on CBS has drawn a bigger Nielsen rating point among young adult viewers than any other late-night talk show. Until now, Jimmy Fallon’s “Tonight Show” on NBC has been the leader in that category, which is vital to advertisers.

Mr. Colbert had a tepid start after his much-ballyhooed debut in September 2015. His show pulled ahead of Mr. Fallon’s in total viewers in February 2017 — the month after President Trump was inaugurated. Between then and the latest Nielsen report, Mr. Fallon had clung to the lead among the 18-to-49-year-old crowd.

The latest season-to-date ratings from Nielsen show that Mr. Colbert has drawn an average of 692,000 adult viewers under 50 during the 2018-2019 season, which began in September. That gives him a slim lead over Mr. Fallon, who averaged 686,000 such viewers in that same period.

Those figures have helped push Mr. Colbert to his first lead as measured by Nielsen rating points, with a margin of 0.54 to 0.53. As New York magazine’s Vulture website reported, Mr. Colbert squeaked past Mr. Fallon in viewers as early as mid-November, but that victory wasn’t sizable enough to give him the lead in the Nielsen numbers.