Red wines and their pomace are valuable sources of phenolic compounds (PCs), which have been proposed as potential contributors to their cardioprotective effect through the inhibition of platelet aggregation. The antiplatelet activity of an extract depends on its chemical composition, specifically the presence of certain phenolic compounds, as well as the interactions between them affecting biological activity. In order to assess the effect on platelet aggregation, we investigated the effect of the grape pomace PC enrichment of a Merlot wine, as well as the effect of the five major phenolic compounds present in wine extracts: caffeic acid, gallic acid, quercetin, epicatechin, and catechin. We analyzed how their combination influenced platelet aggregation. We found that the fortified wine sample with the highest PC content (W8) exhibited a potent antiplatelet effect in aggregation and platelet activation assays induced by the agonists TRAP-6, collagen, and ADP, with its activity being most potent against the latter agonist (78 ± 4%). Among the evaluated phenolic compounds, quercetin showed the highest antiplatelet potential against all three agonists studied, while gallic acid showed minimal antiplatelet effect. These findings suggest that the cardioprotective effect of wines is related to their chemical composition and the synergy among phenolic compounds. However, further research is required to fully understand the underlying mechanisms and clinical relevance of this activity.