LOS ANGELES — A powerful earthquake southeast of Tijuana shook Southern California on Sunday afternoon, damaging buildings in northern Mexico and border cities in California and Arizona and rattling a seismically sophisticated population as far north as Los Angeles and Las Vegas as chandeliers swayed, homes shook and the earth seemed to slide under the feet of people emerging from Easter church services for well over a minute.

The 7.2-magnitude quake struck just after 3:30 p.m. local time, and was centered 16 miles southwest of Guadalupe Victoria in Baja California, Mexico, and about 110 miles southeast of Tijuana, said the United States Geological Survey.

Carlton Hargrave, 64, was standing in the entryway of Family Style Buffet in Calexico, a California border town, when the quake hit. His restaurant, he said in a telephone interview, was “almost completely destroyed.”

Image A man in Calexico, Calif., swept up broken glass after a 7.2 magnitude earthquake struck on Sunday. Credit... Sandy Huffaker/Getty Images

“We’ve got tables overturned, plates broken on the floor, the ceilings caved in,” Mr. Hargrave said with a shaky voice over the sound of his feet crunching rubble and glass. “It was big. I mean, it was major.”