Schlumberger Ltd., the world’s biggest oil-services company by market value, agreed to acquire a minority stake in Eurasia Drilling Co., Russia’s largest onshore drilling firm, for about $1.7 billion.

The move represents an unusually large investment by a U.S.-listed company in Russia’s oil industry, at a time of high tension between Moscow and the West. The investment also comes as oil prices have more than halved since last summer, dragging down shares in the global oil-services sector and spurring consolidation elsewhere....