The mission, which has a mast the length of a school bus, is the first telescope capable of focusing the highest-energy X-ray light into detailed pictures, researchers said.
The new black-hole finds are the first of hundreds expected from the mission over the next two years.
These gargantuan structures - black holes surrounded by thick disks of gas - lie at the hearts of distant galaxies between 0.3 and 11.4 billion light-years from Earth.
"We were looking at known targets and spotted the black holes in the background of the images," said Alexander.
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Additional serendipitous finds such as these are expected for the mission, researchers said.
Along with the mission's more targeted surveys of selected patches of sky, the the Nuclear Spectroscopic Telescope Array, or NuSTAR team plans to comb through hundreds of images taken by the telescope with the goal of finding black holes caught in the background.
By combining observations taken across the range of the X-ray spectrum, the astronomers hope to crack unsolved mysteries of black holes. For example, how many of them populate the universe?
"We are getting closer to solving a mystery that began in 1962," said Alexander.
"Back then, astronomers had noted a diffuse X-ray glow in the background of our sky but were unsure of its origin. Now, we know that distant supermassive black holes are sources of this light, but we need NuSTAR to help further detect and understand the black hole populations," Alexander said.
"The highest-energy X-rays can pass right through even significant amounts of dust and gas surrounding the active supermassive black holes," said Fiona Harrison, a study co-author and the mission's principal investigator at the California Institute of Technology, Pasadena.
The study was published in The Astrophysical Journal.