Worried the ground was unstable, the men were backing the 22-ton engine out when its front end fell into the sinkhole, Matheney said.
The two safely climbed out the windows as water and mud began to fill the vehicle's interior, Matheney said.
Department of Water and Power spokeswoman Kim Hughes said the firefighters were responding to a 6-inch cast iron pipe break on the street. She said water in the area was turned off while tow trucks prepared to pull the engine out of the hole.
Hughes said she didn't know whether the burst water main was related to another one that broke about two miles away over the weekend. The rupture in Studio City on Saturday swept cars down streets, forced people out of their homes and flooded a section of a major boulevard.
The broken main was part of the city's original water system, dating to 1914, and was slated for repair.
Hughes said the main should be in operation Tuesday morning. However, street repairs forced the shutdown of a major road across the Hollywood Hills.