NBC’s “The Tonight Show Starring Jimmy Fallon” comfortably won the late-night ratings race in the young-adult demo during the opening week of the television season, coming within 5% of last year’s result even though CBS saw significant improvement for its “Late Show” with Stephen Colbert.

The new CBS host is clearly bringing a younger audience than the network is accustomed to seeing in late-night, and that’s reflected in the fact that its year-over-year gains vs. David Letterman’s performance a year ago are considerably larger in key demos than total viewers. Last week, “Late Show” got a boost from Tuesday’s appearance by Donald Trump, which was Colbert’s second highest-rated night to date.

According to Nielsen estimates for the Sept. 21-25 frame, “Tonight” averaged a 1.05 rating in adults 18-49 — down just a little from last year’s winning 1.10 average and the highest score for Fallon during a full five-day week since April. (He had a higher average for a four-night week last month that featured Trump and Justin Timberlake as guests.)

“Late Show” averaged a 0.78 rating to place second and surge 70% above last year’s Premiere Week score with Letterman (0.46); the Colbert program was up 8% week-to-week (from 0.72) and this is its best average to start a season since 2011. He was also up 67% vs. last year in both adults 18-34 (0.5 vs. 0.3) and adults 25-54 (1.6 vs. 1.0), giving CBS its best “Late Show” ratings in Premiere Week since 2011 and 2012, respectively. ABC’s “Jimmy Kimmel Live” remained third with a 0.59 rating in 18-49, which is down 11% from last year but is the show’s top weekly average since June.

“Tonight” also led in total viewers (3.58 million, down 8% from last year), followed by “Late Show” (3.22 million, up 19%) and “Kimmel” (2.50 million, down 9%). For “Late Show,” this was its largest Week 1 audience in four years.

In the 11:35 a.m. to 12:35 a.m. timeslot, NBC’s “Late Night With Seth Meyers” won in 18-49 with a 0.54 rating to a 0.38 for CBS’ “Late Late Show with James Corden.” “Late Night” rose 8% above his year-ago premiere (0.50) for his highest-rated five-day week since February, while “Late Late Show” was up 9% from Craig Ferguson’s performance (0.35). Meyers also prevailed in total viewers, 1.515 million to 1.429 million for Corden.

From 12:35 to 1:05 a.m., ABC’s “Nightline” joined Kimmel in having its highest-rated week since June (0.38 in 18-49, 1.595 million viewers overall), down a little from last year. And at 1:35 a.m., NBC’s “Last Call with Carson Daly” (0.35 in 18-49, 0.98 million viewers overall) grew year-to-year by 13% in 18-49 — its highest rating for a full five-day week since last November — and by 18% in total viewers.