LAUREL, Md.—National Aeronautics and Space Administration’s New Horizons spacecraft has survived the most distant exploration of another world, a tiny, icy object 4 billion miles away that looks to be shaped like a peanut or bowling pin.

Word of success came 10 hours after the middle-of-the-night encounter, once flight controllers in Maryland received word from the spacecraft late Tuesday morning. Cheers erupted at Johns Hopkins University’s Applied Physics Laboratory, home to Mission Control, as mission operations manager...