  The recent gravitational wave merger event, GW190521, has challenged our
understanding of the stellar-mass black hole (BH) formation. The primary and
secondary BH are both inferred to fall inside the pair-instability (PI) mass
gap. Here we propose that the formation of such binaries is possible through
gas accretion onto the BH remnants of Population III (Pop~III) stars born in
high-redshift ($z>10$) minihalos. Once the parent halo has grown to the
atomic-cooling limit, even brief episodes of gas accretion in the dense central
regions of the halo can increase the masses of Pop~III remnant BHs above the PI
limit. Starting with a BBH with an initial mass of O(100) ${\rm M_{\odot}}$ we
find that it would only need to spend about 100~Myr in the inner few pc of an
atomic-cooling halo to accrete about 50~${\rm M_{\odot}}$ of material and
resemble a system similar to GW190521. The dynamical friction timescale for the
binary to sink to the dense inner region of its parent halo is comparable or
shorter than the accretion timescale required to increase their mass above the
PI limit. Once in the core of the halo, the binary can enter a phase of
hyper-Eddington accretion, where it would only take a few thousand years to
exceed the PI limit through accretion. Even more massive BBHs could form
through this channel, and be detectable by detectors with improved
low-frequency sensitivity. Single Pop~III BH remnants would also grow through
accretion and could later form binaries dynamically. As little as a few percent
of Pop~III BH remnants may be sufficient to match the rate of massive BBH
mergers inferred from GW190521 of $0.13^{+0.3}_{-0.11}\rm Gpc^{-3} yr^{-1}$.
