Heat-Assisted Extraction (HAE) was used for the optimized production of an extract rich in anthocyanin compounds from Ocimum basilicum var. purpurascens leaves. The optimization was performed using the response surface methodology employing a central composite experimental design with five-levels for each of the assessed variables. The independent variables studied were the extraction time (t, 20–120 min), temperature (T, 25–85 °C), and solvent (S, 0–100% of ethanol, v/v). Anthocyanin compounds were analysed by HPLC-DAD-ESI/MS and the extraction yields were used as response variables. Theoretical models were developed for the obtained experimental data, then the models were validated by a selected number of statistical tests, and finally, those models were used in the prediction and optimization steps. The optimal HAE conditions for the extraction of anthocyanin compounds were: t = 65.37 ± 3.62 min, T = 85.00 ± 1.17 °C and S = 62.50 ± 4.24%, and originated 114.74 ± 0.58 TA mg/g of extract. This study highlighted the red rubin basil leaves as a promising natural matrix to extract pigmented compounds, using green solvents and reduced extraction times. The extract rich in anthocyanins also showed antimicrobial and anti-proliferative properties against four human tumor cell lines, without any toxicity on a primary porcine liver cell line.