Heralded single-photon sources (HSPS) intrinsically suffer from multiphoton emission, leading to a trade-off between the source’s single-photon quality and the heralding rate. A solution to this problem is to use photon-number-resolving (PNR) detectors to filter out the heralding events where more than one photon pair is created. Here, we demonstrate an improvement of a HSPS by heralding photons using a high-efficiency parallel superconducting nanowire single-photon detector (P-SNSPD) with PNR power. Specifically, we show a reduction in the g ( 2 ) ( 0 ) of the heralded single photon by ( 26.9 ± 0.1 ) % for a fixed pump power, or alternatively, an increase in the heralding rate by a factor of 1.368 ± 0.002 for a fixed g ( 2 ) ( 0 ) . We also demonstrate that such a PNR device can reveal thermal photon-number statistics of unheralded photons, which is enabled by our ability to construct its full input–output response function. These results are possible thanks to our P-SNSPD architecture that ensures non-latching operation with no electrical crosstalk, which are essential conditions necessary to obtain the correct photon-number statistics and also faster recovery times, therefore enabling fast heralding rates. These results show that our efficient PNR P-SNSPD architecture can significantly improve the performance of HSPSs and can precisely characterize them, making these detectors a useful tool for a wide range of optical quantum information protocols.