The production of ultra-pure raw material is a crucial step to ensure the required background level in rare event searches. In this work, we establish an innovative technique developed to produce high-purity (99.999%) granular zinc. We demonstrate the effectiveness of the refining procedure by measuring the internal contaminations of the purified zinc with a high-purity germanium detector at the Laboratori Nazionali del Gran Sasso. The total activity of cosmogenic activated nuclides is measured at the level of a few mBq/kg, as well as limits on naturally occurring radionuclides are set to less than mBq/kg. The excellent radiopurity of the zinc sample allows us to search for electron capture with positron emission and neutrinoless double electron capture of 64 Zn, setting the currently most stringent lower limits on their half-lives, T 1 / 2 ε β + > 2.7 × 10 21 year (90% CI), and T 1 / 2 0 ν 2 ε > 2.6 × 10 21 year (90% CI), respectively.