Magnetic fields are ubiquitous in the Universe. Extragalactic disks, halos and clusters have consistently been shown, via diffuse radio-synchrotron emission and Faraday rotation measurements, to exhibit magnetic field strengths ranging from a few nG to tens of $mu$G. The energy density of these fields is typically comparable to the energy density of the fluid motions of the plasma in which they are embedded, making magnetic fields essential players in the dynamics of the luminous matter. The standard theoretical model for the origin of these strong magnetic fields is through the amplification of tiny seed fields via turbulent dynamo to the level consistent with current observations. Here we demonstrate, using laser-produced colliding plasma flows, that turbulence is indeed capable of rapidly amplifying seed fields to near equipartition with the turbulent fluid motions. These results support the notion that turbulent dynamo is a viable mechanism responsible for the observed present-day magnetization of the Universe.