"Before and after" images beamed to Earth showed the results as an indentation on the surface of the rock.
The drill instrument is capable of both hammering and rotating actions, and if the rock is determined to be a good candidate for the rover's scientific work, a number of test holes will be drilled, NASA said, to create samples for delivery to the rover's onboard laboratories.
They would be analyzed as part of the rover's main mission to determine whether the Gale location has ever been capable of supporting bacterial life.
"The rock is behaving well and it looks pretty soft, so that's encouraging," Curiosity project scientist Professor John Grotzinger told BBC News.
The first drilling is being carried out on a very fine-grained sedimentary rock, NASA said.
"The drilling is going very well so far and we're making great progress with the early steps," Grotzinger said.