JAKARTA, Indonesia—A mobile browser rarely used in the West has outflanked Google’s Chrome in some of Asia’s fastest-growing markets, giving owner Alibaba Group Holding Ltd. an advantage in the race among technology giants to capture the next generation of internet users.

Hundreds of millions of people in India, Indonesia and other emerging markets getting online for the first time are picking UC Browser, owned by Chinese e-commerce giant Alibaba, over ones made by U.S. rivals. Users say UC Browser works better in countries...