Inland waters are an important component of the global carbon budget, emitting CO₂ to the atmosphere. However, our ability to predict carbon fluxes from stream systems remains uncertain as small scales of pCO₂ variability within streams (10⁰-10² m), which makes efforts relying on monitoring data uncertain. 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 (WC), and benthic hyporheic zone (BHZ) respiration, downstream advection, and atmospheric exchange. We evaluate this model against existing statistical methods including upscaling and multiple linear regressions through comparisons to high-resolution stream pCO₂ data collected across the East River Watershed in the Colorado Rocky Mountains (USA). 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 suggesting that streams transition from GW- to BHZ-dominated sources between 3^rd and 4^th Strahler orders, with GW, BHZ, and WC accounting for 49.3, 50.6, and 0.1% of CO₂ fluxes from the watershed, respectively. Lastly, stream network model CO₂ fluxes are 4-12x times smaller than upscaling technique predictions, largely due to inverse correlations between stream pCO₂ and atmosphere exchange velocities. Taken together, this stream network model improves our ability to predict stream CO₂ dynamics and efflux. Furthermore, future applications to regional and global scales may result in a significant downward revision of global flux estimates.