On the highlands of Mars early in the history of the planet precipitation-driven fluvial erosion competed with ongoing impact cratering. This disruption, and the multiple enclosed basins produced by impacts, is partially responsible for a long debate concerning the processes and effectiveness of fluvial erosion. The role of fluvial erosion in sculpting the early Martian landscape is explored here using a simulation model that incorporates formation of impact craters, erosion by fluvial and slope processes, deposition in basins, and flow routing through depressions. Under assumed arid hydrologic conditions, enclosed basins created by cratering do not overflow, drainage networks are short, and fluvial bajadas infill crater basins with sediment supplied from erosion of interior crater slopes and, occasionally from adjacent steep slopes. Even under arid conditions adjacent crater basins can become integrated into larger basins through lateral erosion of crater rims or by rim burial by sediment infilling. Fluvial erosion on early Mars was sufficient to infill craters of 10 km or more in diameter with 500–1500 m of sediment. When the amount of runoff relative to evaporation is assumed to be larger, enclosed basins overflow and deeply incised valleys interconnect basins. Examples of such overflow and interconnection on the Martian highlands suggest an active hydrological cycle on early Mars, at least episodically. When fluvial erosion and cratering occur together, the drainage network is often disrupted and fragmented, but it reintegrates quickly from smaller impacts. Even when rates of impact are high, a subtle fluvial signature is retained on the landscape as broad, smooth intercrater plains that feature craters with variable amounts of infilling and rim erosion, including nearly buried “ghost” craters. The widespread occurrence of such intercrater plains on Mars suggests a strong fluvial imprint on the landscape despite the absence of deep, integrated valley networks. Indisputable deltas and alluvial fans are rare in the crater basins on Mars, in part because of subsequent destruction of surficial fluvial features by impact gardening and eolian processes. Simulations, however, suggest that temporally-varying lake levels and a high percentage of suspended to bedload supplied to the basins could also result in poor definition of fan–delta complexes.