This is the first time any robot has drilled into a rock to collect a sample on Mars, the US space agency said.
The fresh hole, about 0.63 inch wide and 2.5 inches deep in a patch of fine-grained sedimentary bedrock, can be seen in latest images and other data Curiosity beamed to Earth.
The rock is believed to hold evidence about long-gone wet environments. In pursuit of that evidence, the rover will use its laboratory instruments to analyse rock powder collected by the drill.
"This is the biggest milestone accomplishment for the Curiosity team since the sky-crane landing last August, another proud day for America," said John Grunsfeld, NASA associate administrator for Science Mission Directorate.
For the next several days, ground controllers will command the rover's arm to carry out a series of steps to process the sample, ultimately delivering portions to the instruments inside.
"We commanded the first full-depth drilling, and we believe we have collected sufficient material from the rock to meet our objectives of hardware cleaning and sample drop-off," said Avi Okon, drill cognizant engineer at NASA.
Rock powder generated during drilling travels up flutes on the bit. The bit assembly has chambers to hold the powder until it can be transferred to the sample-handling mechanisms of the rover's Collection and Handling for In-Situ Martian Rock Analysis (CHIMRA) device.
Before the rock powder is analysed, some will be used to scour traces of material that may have been deposited onto the hardware while the rover was still on Earth, despite thorough cleaning before launch.
"We'll take the powder we acquired and swish it around to scrub the internal surfaces of the drill bit assembly," said JPL's Scott McCloskey, drill systems engineer.
"Then we'll use the arm to transfer the powder out of the drill into the scoop, which will be our first chance to see the acquired sample," said McCloskey.
"Building a tool to interact forcefully with unpredictable rocks on Mars required an ambitious development and testing program," said JPL's Louise Jandura, chief engineer for Curiosity's sample system.
"To get to the point of making this hole in a rock on Mars, we made eight drills and bored more than 1,200 holes in 20 types of rock on Earth," Jandura said.