Inland waters are recognized as a significant source of CO₂ to the atmosphere; however, the global magnitude of this flux remains uncertain. In particular, CO₂ concentrations and fluxes in stream systems are extremely variable at scales of 10’s to 100’s of meters, complicating monitoring and prediction efforts. Thus, models of pCO₂ that capture these scales of spatial variability are necessary for the accurate prediction and monitoring of stream CO₂ fluxes. Despite a strong conceptual framework for the hydrologic processes that control stream CO₂, predictive models to date have been empirical, based on Strahler stream order and regressions between observed pCO₂ and landscape variables. We hypothesize that models incorporating well-described hydrologic processes may lead to new insights into the magnitude of various CO₂ sources and improve predictions. Here, we develop and apply a process-based stream network model of CO₂ based on NHDplus flowlines and driven by groundwater inputs, hyporheic exchange, water-column metabolism, advective transport, and atmospheric exchange. Model output is compared with 151 measurements of pCO₂ (424 - 9718 ppm) collected in August, 2019 across the upper East River watershed in Gothic, CO, a mountainous, high-elevation headwaters system within the Colorado River basin. We find that modeled pCO₂ captures observed spatial patterns and predicts measured values with a RMSE of ~250 ppm and R² of 0.47 (p<10^-15). Additionally, our process-based model performs significantly better than a multiple linear regression model between observations and a geomorphic variables (r²=0.35, p<10^-7). Estimates from an optimized stream network model give additional insight into CO₂ sources, suggesting that groundwater accounts for 70-80% of evasion fluxes, hyporheic processes for 20-30%, and water-column metabolism for ~1% across the East River watershed. The ability of our model to predict pCO₂ at the spatial scales of variability may provide an important next step in estimating global CO₂ fluxes, and future research will test the predictive power of process-based models at regional and global scales.