The gravity-boost took place about halfway through the two-year journey of the spacecraft, known as OSIRIS-REx (Origins, Spectral Interpretation, Resource Identification, and Security - Regolith Explorer).
"The preliminary results are in, and my #EarthGravityAssist was succesful!" said the NASA Twitter account for OSIRIS-REx, about an hour after it made its closest approach to Earth at 12:52 pm (1652 GMT).
The mission launched last year from Cape Canaveral, Florida. Its goal is to collect a sample from Bennu in 2018, and return it to Earth for further study in 2023.
Dante Lauretta, OSIRIS-REx principal investigator at the University of Arizona, Tucson, described the gravity-assist as "a clever way to move the spacecraft onto Bennu's orbital plane using Earth's own gravity instead of expending fuel."
The spacecraft zipped over Antarctica at a distance of 11,000 miles (17,000 kilometers), using Earth's gravity to shift its trajectory so it can eventually meet up with Bennu.
The asteroid's orbit around the Sun is tilted six degrees in comparison to Earth's.
During the gravity assist, OSIRIS-REx swung through a region of space that contains Earth-orbiting satellites, but emerged intact.
OSIRIS-REx lost communications with Earth for about an hour during the flyby, as expected, because the spacecraft was too low relative to the southern horizon to be in view with either the Deep Space tracking station at Canberra, Australia, or Goldstone, California.
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