One week does not a trend make, but the latenight signs are encouraging for CBS.

The Eye’s “Late Show With David Letterman,” boosted by guest appearances by Presidents Obama and Clinton on the opening nights of the season, pulled ahead of “The Tonight Show” in key demos during premiere week — the show’s first victory in four years over the longtime latenight leader.

“Late Show” built on its presidential firepower to start the week by prevailing over “Tonight” in adults 18-49 on every night of the Sept. 21-25 frame (including a tie on Tuesday with Clinton). This is noteworthy because prior to last week, Letterman hadn’t won a single night opposite a firstrun seg of the Conan O’Brien-led “Tonight Show.”

(Note that O’Brien did air one repeat last week, an unscheduled one on Friday due to his head injury while taping the show.)

The ratings shift coincides with NBC’s softness at 10 p.m. leading into the late local newscasts with its new “The Jay Leno Show.” While O’Brien’s “Tonight Show” was consistently winning in the summer when no net had much of an edge in the final hour of primetime, CBS figures to consistently enjoy a real advantage at 10 p.m. over Leno with its strong lineup of dramas.

According to Nielsen estimates that include same-night DVR playback, “Late Show” averaged a 1.3 rating in adults 18-49 and 5.04 million viewers overall during premiere week to a 1.0 demo rating for “Tonight” and 2.40 million total viewers. (The Obama visit on Monday averaged a big 2.0 rating, providing Letterman with a big cushion for the frame.)

The CBS show was up 18% in 18-49 vs. premiere week last year while “Tonight” was down 23% vs. last year when Leno hosted.

“Late Show” has been regularly beating “Tonight” in total viewers in recent months, but its premiere-week margin of victory in overall audience — more than doubling its rival –marked the program’s largest advantage since February 1994 (when CBS aired the massively rated Winter Olympics from Lillehammer).

CBS also has reason to crow about the 12:35 a.m. performance of “The Late Late Show With Craig Ferguson,” which tied NBC’s “Late Night With Jimmy Fallon” in adults 18-49 during premiere week (0.6 rating) while winning outright in adults 25-54 (0.8 to 0.7) and total viewers (2.11 million to 1.40 million).

“It’s only one week, but it’s a great way to start the new season,” said Nina Tassler, CBS Entertainment prexy. “We think our guys in latenight are putting on great shows, and we like the ratings trends that we’re seeing.”

ABC’s half-hour “Nightline” (airing at 11:35 p.m.), averaged 4.23 million viewers, a 1.1 rating in 18-49 and a 1.5 rating in adults 25-54 — up a bit in total viewers and down slightly in demos. This was the show’s best 25-54 score in eight months and its largest overall aud in nearly a year.

And “Jimmy Kimmel Live” (12:05-1:05 a.m.) was on par with last year, averaging 1.80 million viewers and a 0.6 rating in 18-49.