Arctic tundra has the potential to generate significant climate feedbacks, but spatial complexity makes it difficult to quantify the impacts of climate on ecosystem-atmosphere fluxes, particularly in polygonal tundra comprising wetter and drier polygon types on the scale of tens of meters. We measured CO2, CH4, and energy fluxes using eddy covariance for 7 yr (April to November, 2013–2019) in polygonal tundra near Utqiagvik, Alaska. This period saw the earliest snowmelt, latest snow accumulation, and hottest summer on record. To estimate fluxes by polygon type, we combined a polygon classification with a flux-footprint model. Methane fluxes were highest in the summer months but were also large during freeze-up and increased with the warming trend in August–November temperatures. While CO2 respiration had a consistent, exponential relationship with temperature, net ecosystem exchange was more variable among years. CO2 and CH4 exchange (June–September) ranged between −0.83 (Standard error [SE] = 0.03) and −1.32 (SE = 0.04) μmol m−2 s−1 and 13.92 (SE = 0.26)—23.42 (SE = 0.45) nmol m−2 s−1, respectively, and varied interannually (p ≤ 0.05). The maximum-influence method effectively attributed fluxes to polygon types. Areas dominated by low-centered polygons had higher CO2 fluxes except in 2016–2017. Methane fluxes were highest in low-centered polygons 2013–2015 and in flat-centered polygons in subsequent years, possibly due to increasing temperature and precipitation. Sensible and latent heat fluxes also varied significantly among polygon types. Accurate characterization of Arctic fluxes and their climate dependencies requires spatial disaggregation and long term observations.