Biphotons and single photons with narrow bandwidths and long coherence times are essential to the realization of long-distance quantum communication (LDQC) and linear optical quantum computing (LOQC). In this Letter, we manipulate the biphoton wave functions of the spontaneous four-wave mixing in a two-level atomic ensemble with a single-laser pump scheme. Our innovative experimental approach enables the generation of biphotons with a sub-MHz bandwidth of 0.36 MHz, a record spectral brightness of 2.28×10^{7} s^{-1} mW^{-1} MHz^{-1}, and a temporally symmetric wave packet at moderate optical depth. The strong nonclassical cross-correlation of the biphotons also enables the observation of heralded sub-MHz-linewidth single photons with a pronounced single-photon nature. The generation of sub-MHz-linewidth biphotons and single photons with a two-level atomic ensemble not only finds applications in quantum repeaters and large cluster states for LDQC and LOQC but also opens up the opportunity to miniaturize the biphoton or single-photon sources for chip-scale quantum technologies.