The robot's tool bit hammered briefly, without rotation, into a flat slab of rock on the floor of Gale Crater, the huge bowl where it landed last August.
Although previous rovers have scrubbed the surface of rocks, Curiosity is the first to carry the capability to drill inside them.
Pictures taken before and after the operation reveal the indentation left by the tool's action, BBC News reported.
NASA engineers are taking a step-by-step approach to the procedure as they need to check both the rock and the drill are behaving as expected.
If the target slab is deemed suitable, a number of test holes are likely to be drilled - using the rotation as well the percussive action - before a powdered sample is picked up and delivered to Curiosity's onboard laboratories.
The rover's mission is to try to determine whether Gale has ever had the environments in the past that were capable of supporting bacterial life, the report said.
Detailing the composition of rocks is critical to this investigation as the deposits in the crater will retain a geochemical record of the conditions under which they formed.
Drilling a few centimetres inside a rock provides a fresh sample that is free from the alteration that can occur at the surface as a result of weathering or radiation damage.
Curiosity landed on the Red Planet on 6 August last year. It has since driven east of its touchdown point to a location that satellite images had identified as an intersection of three distinct geological terrains.
The robot is currently in a small depression dubbed Yellowknife Bay. The rock selected for the first drilling is a very fine grained sedimentary rock cut through with veins of what appear to be a calcium sulphate.
This rock also has a name - John Klein, taken from a recently deceased NASA engineer who worked on the rover project.
Scientists are thrilled with the progress of the mission so far. Many of the rocks, like the ones in Yellowknife Bay, show clear evidence of deposition in, or alteration by, water.
