Cook-vide (CV, vacuum boiling) and sous-vide (SV, cooking in a vacuum-sealed pouch) have been applied to cook purple-flesh potatoes. Response surface methodology (RSM) sets up the work conditions of temperatures (78–92 °C) and times (16–44 min). Textural parameters, colour and anthocyanins have been measured in cooked samples, and microstructure of cooked tissues was observed with cryo-SEM technique. CV and SV provided similar hardness (P > 0.05), while SV treatments provided samples more adhesive and cohesive than CV ones (P ≤ 0.05). Micrographs of cooked samples showed rounder cells in cook-vide samples and higher swelling than in sous-vide ones. SV treatment avoided the leaching into the water of anthocyanins (chromophore) retaining more of them in potatoes (P ≤ 0.05), as a consequence of which total colour difference was lower in SV samples compared with CV ones (P ≤ 0.05). Particularly, CV samples were lighter (higher values of L*) and less reddish (lower values of +a*) than SV ones (P ≤ 0.05).