“It is amazing to be here,” said Pedro Pascal in his first “Saturday Night Live” performance: a triumphant Season 48 episode for the sketch show, cross-promoting the actor/host’s hugely successful parts on Disney’s “The Mandalorian” and HBO’s “The Last of Us.”

“I was born in Chile and nine months later my parents fled Pinochet with me and my sister to the US,” Pascal continued in his opening monologue. “They were so brave, and without them I wouldn’t be here in this wonderful country. And I certainly wouldn’t be standing here with you all tonight.”

The 48-year-old actor began performing on screen in the late ’90s, appearing in “Buffy the Vampire Slayer” and “NYPD Blue” among other popular TV series of the time. Pascal made his feature film debut in Julia Solomonoff’s “Hermanas” in 2005, and would later appear in “The Adjustment Bureau,” “Sweet Little Lies,...