An early winner from the latest round of Iranian sanctions is emerging: Russia.

The U.S. began enforcing a tough new slate of economic restrictions against Iran on Monday, including a threat to sanction buyers of Iranian crude. That has refineries in Europe and Asia—recent, big buyers of Iran oil—looking for alternative supplies. Russian oil companies have stepped in, stealing customers from Iran. The two countries produce similar grades of crude, making a switch by refiners relatively easy.

But...