Weeds represent a serious drawback affecting the productivity of field crops worldwide. While the most common approach to control weeds in no-till practices is the use of glyphosate-based herbicides (GBHs), reducing their use represents a major challenge. This two-year field study aims to evaluate whether the use of cover crops (CC) in transgenic soybean and corn productions can (1) help control weeds and (2) reduce the amount of GBH needed for managing weeds. Sampling was carried out in 32 experimental field plots (four crop managements with four replicates on both crops). Crop managements consisted of GBH applications at rates of 0.84, 1.67, and 3.3 L ha−1 in plots in direct seeding with CC (DSCC) and at rates of 3.3 L ha−1 in plots without CC (DS). Weed cover rates, plant parameters (fresh and dry weights and heights), grain yields, water, and cation contents in soil were considered as indicators of interspecific competition. Results obtained in both years show that it is possible to reduce GBH use by 50% in plots with CC compared to plots without CC using a rate of GBH application of 3.33 L ha−1 (DS 3.3). However, weeds had a large impact on water content in soil, which was reflected by smaller plants and lower yields in plots with only 0.84 L ha−1 of GBH applied. In the context of the study, the use of CCs seems to facilitate the development of more sustainable agriculture while reducing the quantities of GBH generally used.