Natural covering (NATC) has spread on hillside vineyards of central Italy as a replacement for tillage to reduce soil erosion, although it increased nitrogen and water needs. Therefore, in the current context of global warming, using cover crops (CCs) that require less water and provide nitrogen becomes crucial. The effects of two low-competition legume-enriched CCs in a rainfed hillside vineyard—a perennial legume–grass mixture (PLGM) and an annual legume cover crop of Trifolium alexandrinum (ALTA)—were compared with NATC over three years. PLGM and ALTA provided good levels of soil coverage, slightly lower than NATC, which had a negligible presence of legumes. PLGM and ALTA, due to low competition, enhanced vine vigor, resulting in thicker and wider canopies (as indicated by total leaf area and leaf layer number), higher pruning weight, and increased yield. PLGM and ALTA led to good qualitative levels, with higher grapes acidities, lower pH and total soluble solids content and, additionally, significantly higher yeast assimilable nitrogen content. In conclusion, implementing low-competition legume species in CCs is an effective tool to avoid soil erosion in a climate change scenario, leading to increased productivity, higher acidity, and improved nitrogen content in the grapes.