The American space agency's Dawn spacecraft is bearing down on Ceres, the largest object in the asteroid belt between Mars and Jupiter.
New pictures released on Monday will help navigators put the satellite on the correct path to go into orbit around the dwarf planet on 6 March.
Come the end of the month, the probe's pictures will better those from Hubble.
At the moment, at a separation of just under 400,000km, they are still only 80% as sharp as what the famous space telescope can produce.
Ceres will be the first dwarf planet to be visited up-close. The second encounter will come in July when Nasa's New Horizons spacecraft flies by Pluto.
The dwarfs are a distinct class of object in the Solar System - after the terrestrial inner planets like Earth and the gas giants like Jupiter.
Dawn is arriving at Ceres after visiting the asteroid Vesta. This 530km-wide rock had the look of a punctured football, the result of a colossal collision sometime in its past that ripped a big chunk out of its southern polar region.
Ceres, on the other hand, is big enough for gravity to have pulled it into a more spherical shape.
Scientists think both bodies are fledglings that never quite made it to the planetary big time.
In the case of Vesta, it underwent a lot of the same processes that transformed the early Earth, such as differentiating its insides to include an iron core. In contrast, Ceres' bid to reach the major planet league probably stalled very quickly.
Researchers believe its interior is dominated by a rocky core topped by ice that is then insulated by rocky lag deposits at the surface. A big question the mission hopes to answer is whether there is a liquid ocean of water at depth. Some models suggest there could well be.
Dawn is supposed to undertake a 16-month study of Ceres once it gets into orbit, but that may depend on how well the hobbled probe performs.
It has lost two of the four reaction wheels it uses for fine-pointing. As a result, it has to fire its thrusters to maintain a correct attitude, but this puts a drain on its hydrazine fuel supply. If everything keeps working, observations will be made from as low as 400km from the surface.
When time is eventually called on the mission, Dawn will be left circling Ceres.
"They've run out the models for a hundred years and it'll be a very stable orbit. We'll become a perpetual satellite of Ceres," deputy principal investigator Carol Raymond told BBC News.
Jonathan.Amos-INTERNET@bbc.co.uk and follow me on Twitter: @BBCAmos