U.S. oil prices rose above $70 for the first time since 2014, the latest sign that buoyant economic growth and investor concern about the risk of Middle East conflict are once again reshaping the global energy industry.

The $70-a-barrel milestone represents a victory for Saudi Arabia, which in late 2016 spearheaded a landmark production-cutting deal between the Organization of the Petroleum Exporting Countries and other major producers, including Russia. That helped dry up a massive glut of oil more quickly than many on Wall...