Arctic tundra ecosystems are currently facing amplified rates of climate warming. Since these ecosystems store significant amounts of soil organic carbon, which can be mineralized to carbon dioxide (CO2) and methane (CH4), rising temperatures may cause increasing greenhouse gas fluxes to the atmosphere. To understand how net the ecosystem exchange (NEE) of CO2 will respond to changing climatic and environmental conditions, it is necessary to understand the individual responses of the processes contributing to NEE. Therefore, this study aimed to partition NEE at the soil–plant–atmosphere interface in an arctic tundra ecosystem and to identify the main environmental drivers of these fluxes. NEE was partitioned into gross primary productivity (GPP) and ecosystem respiration (Reco) and further into autotrophic (RA) and heterotrophic respiration (RH). The study examined CO2 flux data collected during the growing season in 2015 using closed-chamber measurements in a polygonal tundra landscape in the Lena River Delta, northeastern Siberia. To capture the influence of soil hydrology on CO2 fluxes, measurements were conducted at a water-saturated polygon center and a well-drained polygon rim. These chamber-measured fluxes were used to model NEE, GPP, Reco, RH, RA, and net primary production (NPP) at the pedon scale (1–10 m) and to determine cumulative growing season fluxes. Here, the response of in situ measured RA and RH fluxes from permafrost-affected soils of the polygonal tundra to hydrological conditions have been examined. Although changes in the water table depth at the polygon center sites did not affect CO2 fluxes from RH, rising water tables were linked to reduced CO2 fluxes from RA. Furthermore, this work found the polygonal tundra in the Lena River Delta to be a net sink for atmospheric CO2 during the growing season. The NEE at the wet, depressed polygon center was more than twice that at the drier polygon rim. These differences between the two sites were caused by higher GPP fluxes due to a higher vascular plant density and lower Reco fluxes due to oxygen limitation under water-saturated conditions at the polygon center in comparison to the rim. Hence, soil hydrological conditions were one of the key drivers for the different CO2 fluxes across this highly heterogeneous tundra landscape.