Direct numerical simulation (DNS) coupling with chemistry coordinate mapping (CCM) is presented to simulate flame propagation and auto-ignition in a partially premixed syngas/air mixture. In the CCM approach, the physical domain is mapped into a low dimensional phase space with a few thermodynamic variables as the independent variables. The integration of the chemical reaction rates and heat release rate are done on the grid in the phase space. Previously we showed that for premixed mixtures, two variables temperature and specific element mass fraction of H atom, can be sufficient to construct the phase space for a satisfactory mapping. However, for partially premixed combustion mode, a third phase space variable is required to map the physical cell into the phase space. It is shown that scalar dissipation rate of the element mass ratio of H atom can be used as the third dimension of the phase space. An investigation is carried out on the behavior of CCM and the choice over the element on which the local element mass ratio should be based. Mapping error in the CCM is investigated. It is shown that if the element mass ratio is based on the element involved in the most diffusive molecules, the error of the mapping can approach zero when the grid in the phase space is refined. To validate the CCM approach the results of DNS coupled with CCM (DNS-CCM) are compared with full DNS that integrates the chemical reaction rates and heat release rate directly in physical space. Good agreement between the results from DNS and DNS-CCM is obtained while the computational time is reduced at least by 70 %.