HOUSTON—BP PLC had its first breakthrough in the effort to stem the oil spill in the Gulf of Mexico, using robots to insert one end of a mile-long tube into a shattered oil pipe on the ocean floor. The goal is to siphon up some, if not most, of the crude gushing into the Gulf of Mexico.

In an early sign of success, BP said it had begun burning off natural gas emerging from the apparatus at the ocean's surface.

At...