Orthogonal to guided growth of nanoparticle (NP) crystals using DNA or supramolecules, a trace amount of polymeric impurities (<0.1 wt.%) leads to reproducible, rapid growth of 3D NP crystals in solution and on patterned substrates with high yield. When polymers preferentially precipitate on the NP surfaces, small NP clusters form and serve as nuclei for NP crystal growth in dilute solutions. This precipitation-induced NP crystallization process is applicable for a range of polymers, and the resultant 3-D NP crystals are tunable by varying polymeric additives loading, solvent evaporation rate, and NP size. The present study elucidates how to balance cohesive energy density and NP diffusivity to simultaneously favor nuclei formation energetically and kinetic growth in dilute solutions to rapidly crystalize NPs over multiple length scales. Furthermore, the amount of impurities needed to grow NP crystals (<0.1%) reminds us the importance of fine details to interpret experimental observations in nanoscience.