The real test for Jimmy Fallon comes next week and beyond, but there’s no denying that the new host of “The Tonight Show” delivered a strong first-week performance.

Friday’s edition of the show — which featured Justin Timberlake, who is known for doing great sketches with Fallon —   delivered 8.77 million viewers and a 2.9 rating in adults 18-49, the highest mark in the key demo since Fallon’s debut outing on Monday.

Fallon’s premiere week was, of course, buoyed by Olympic-size lead-ins, a strategic decision in the timing of “The Tonight Show” handoff that has paid off handsomely for NBC, even if Winter Olympics ratings overall have been mostly ho-hum.

With “Tonight Show” hitting its highest marks in more than 20 years in key measures, NBC execs undoubtedly are hoping that the regime-change at its latenight institution will stick this time around. In June 2009, when Conan O’Brien took the reins from Jay Leno, he did not have the benefit of Olympics lead-ins to boost overall sampling.

Fallon’s “Tonight Show” delivered its most-watched week since May 17-21, 1993, the week of the “Cheers” finale. Friday’s edition was the first of the week that was not pushed to midnight by Olympics coverage. It began at 11:30 p.m., close to the 11:35 p.m. slot that will be the norm for Fallon starting next week.

For the week, Fallon averaged 8.49 million viewers and a 2.8 rating. In the demo that marked the best week for the show since January 2005, when Leno delivered a tribute to Johnny Carson.

There was more good news for Fallon on Friday as Nielsen’s Live-plus-3 numbers boosted his opening night rating to a 4.9 in adults 18-49, up from 3.8 in live-plus-same day measure. That lift makes Fallon’s debut the most-watched Monday seg of “Tonight Show” since May 25, 1992 — the night of Leno’s premiere.

NBC also noted that the live-plus-3 numbers for Leno’s Feb. 6 farewell episode boosted the demo rating to 4.4, from 3.8. That was enough to make it the top Thursday edition of “Tonight” since the night of the “Friends” finale on May 6, 2004.