When Nicole Parlapiano joined Tubi as its marketing chief two years ago, one of the most searched questions about the decade-old streaming service was, “Is it a scam?” It was free, after all, and consumers were skeptical.

“Would it put a virus on your computer?” Ms. Parlapiano said. “People wouldn’t even touch it.”

That’s not an issue now.

Tubi has exploded in popularity over the last 18 months, establishing itself as one of the most popular streaming outfits in the United States. It now consistently outranks Peacock, Max, Paramount+ and Apple TV+ in total viewing time, according to Nielsen — and is drawing even with Disney+. Only YouTube, Netflix, Amazon and Hulu are still ahead.

The streaming service, which is owned by the Fox Corporation, runs a different business model from those competitors. In addition to being free — with revenue coming from advertising — it doesn’t require an account to use, making it more similar to services like Roku and Pluto. And it comfortably commands more engagement than those peers, according to Nielsen.

“We’re like the little engine, and it’s just getting better and better,” Anjali Sud, Tubi’s chief executive, said.

Its sudden rise has come as something of a shock to many competitors, as well as investors.

Unlike its biggest rivals, which allocate huge budgets for original programs or premium sports rights like the N.F.L or the N.B.A., Tubi’s library contains tens of thousands of older shows and movies, many that seem to have been collected from the bargain bin. Some popular programs on the service include the 1970s procedural “Columbo,” and an early 2000s UPN sitcom, “Everybody Hates Chris.”