Recent observations of the high-redshift universe have uncovered a significant number of active galactic nuclei, implying that supermassive black holes (SMBHs) would have to have been formed at much earlier times than expected. Direct collapse of metal-free gas clouds to SMBHs after recombination could help explain the early formation of SMBHs, but this scenario is stymied by the fragmentation of the clouds due to efficient molecular hydrogen cooling. We show that a subdominant population of tiny, evaporating primordial black holes, with significant clustering in some gas clouds, can heat the gas sufficiently so that molecular hydrogen is not formed, and direct collapse to black holes is possible even at high redshifts.