DUBAI, United Arab Emirates— Reformist candidate Masoud Pezeshkian won Iran’s runoff presidential election Saturday, besting hard-liner Saeed Jalili by promising to reach out to the West and ease enforcement on the country’s mandatory headscarf law after years of sanctions and protests squeezing the Islamic Republic.

Pezeshkian promised no radical changes to Iran’s Shiite theocracy in his campaign and long has held Supreme Leader Ayatollah Ali Khamenei as the final arbiter of all…