Zarins is ethnically Latvian, but was born in Germany at the end of the Second World War. His parents emigrated to the United States soon after he was born. He graduated from high school in Lincoln, Nebraska in 1963 and earned a B.A. in anthropology from the University of Nebraska in 1967. He served in the U.S. Army in Vietnam before completing his Ph.D. in Ancient Near Eastern Languages and Archaeology at the University of Chicago in 1974. He then served as archaeological adviser to the Department of Antiquities of the Kingdom of Saudi Arabia before coming to Missouri State in 1978.
Zarins has extensive experience in archaeological fieldwork in Saudi Arabia, Egypt, and Oman, and is now involved in a new project in Yemen. He was chief archaeologist for the Transarabia Expedition which made the famous discovery of the ancient city of Ubar in 1992. This made the headline of the New York Times, and it was also named one of the ten most important discoveries of the year by Discover, Time, and Newsweek magazines. The expedition was featured in a NOVA program called "In Search of the Lost City," which was first broadcast in 1996.
Zarins has published many articles on a number of topics concerning the archaeology of the Near East, which include the domestication of the horse, early pastoral nomadism, and the obsidian, indigo, and frankincense trades. He received an Excellence in Research Award from Missouri State in 1988. He has proposed that the Semitic languages arose as a result of a circum Arabian nomadic pastoral complex, which developed in the period of the desiccation of climates at the end of the pre-pottery phase in the Ancient Near East.
Zarins argued that the Garden of Eden was situated at the head of the Persian Gulf, where the Tigris and Euphrates Rivers run into the sea, from his research on this area using information from many different sources, including LANDSAT images from space. In this theory, the Bible’s Gihon River would correspond with the Karun River in Iran, and the Pishon River would correspond to the Wadi Batin river system that once drained the now dry, but once quite fertile central part of the Arabian Peninsula. His suggestion about the Pishon River is supported by James. A Sauer (1945–1999) formerly of the American Center of Oriental Research  although strongly criticized by the archaeological community.
- Interview with Dr Zarins on the Ubar Expedition
- James A. Sauer, "The River Runs Dry," Biblical Archaeology Review, Vol. 22, No. 4, July/August 1996, pp. 52–54, 57, 64