LIMA, Peru—Venezuelans fleeing their country’s economic collapse have brought an export that is baffling this soccer-mad nation: baseball.

Raul Carrera, a 52-year-old taxi driver, recently watched his first game, a contest between a team of Venezuelan migrants called the Caribeños and Peru’s national team, a collection of amateurs that got outscored 50-0 in a regional tournament a couple of years ago.

Sitting in the drizzling rain at a new stadium, Mr. Carrera was amused by the catcher flashing signals to the pitcher and impressed by the Venezuelan pitcher’s quick throws to catch runners leading too far off first.

“The pitcher has to be extremely intelligent,” said Mr. Carrera, who recalls seeing baseball on TV once before quickly changing channels. “That much I understand.”

Nearly 800,000 Venezuelans have settled in Peru, part of a wider migration of some four million Venezuelans in recent years. The new arrivals have brought Caribbean culture, their arepa corncakes and a passion for baseball, a sport with some history in Peru but a tiny following. Here, as in all of South America except for Venezuela, soccer is king.