Dynamic nuclear polarization DNP effects are observed of 67Zn (I=5/2) nuclear spins in ZnO nanoparticles and of ¹H (I=1/2) spins of the Zn(OH)₂ capping layer. The almost complete polarization of these nuclear spins is achieved by saturating the electron paramagnetic resonance transition of the shallow interstitial Li donor present in the ZnO nanoparticles. The remarkable aspect is that this DNP is caused by an Overhauser mechanism although the phonons mediating the polarization process do not fit into the nanoparticles. An explanation of this DNP process is presented, and it is shown that this allows for a measurement of the distribution of phonon modes in the nanoparticles. The enhancement of the nuclear polarization also opens the possibility to study semiconductor nanostructures with NMR techniques.