Rivers and streams are an important component of the global carbon budget, emitting CO₂ to the atmosphere. However, our ability to accurately predict carbon fluxes from stream systems remains uncertain due to small scales of pCO₂ variability within streams (10⁰-10² m), which make monitoring intractable. Here we incorporate CO₂ input and output fluxes into a stream network advection-reaction model, representing the first process-based representation of stream CO₂ dynamics at watershed scales. This model includes groundwater (GW) CO₂ inputs, water column and benthic hyporheic zone (BZ) respiration, downstream advection, and atmospheric exchange. We evaluate this model against existing statistical methods including upscaling techniques and multiple linear regression models through comparisons to high-resolution stream pCO₂ data collected across the East River Watershed in the Colorado Rocky Mountains. The stream network model accurately captures topography-driven pCO₂ variability and significantly outperforms multiple linear regressions for predicting pCO₂. Further, the model provides estimates of CO₂ contributions from internal versus external sources and suggests that streams transition from GW- to BZ-dominated sources between 3^rd and 4^th Strahler orders, with GW and BZ accounting for 53 and 47% of CO₂ fluxes from the watershed, respectively. Lastly, stream network model CO₂ fluxes are 5-13x times smaller than upscaling technique predictions, largely due to inverse correlations between stream pCO₂ and atmosphere exchange velocities. Taken together, the stream network model presented improves our ability to predict and monitor stream CO₂ dynamics, and future applications to regional and global scales may result in a significant downward revision of global flux estimates.