Fresh pasta was formulated by replacing wheat semolina with 0, 5, 10, and 15 g/100 g (w/w) of Moringa oleifera L. leaf powder (MOLP). The samples (i.e., M0, M5, M10, and M15 as a function of the substitution level) were cooked by boiling. The changes in the phenolic bioaccessibility and the in vitro starch digestibility were considered. On the cooked-to-optimum samples, by means of ultra-high-performance liquid chromatography-quadrupole time-of-flight (UHPLC-QTOF) mass spectrometry, 152 polyphenols were putatively annotated with the greatest content recorded for M15 pasta, being 2.19 mg/g dry matter (p < 0.05). Multivariate statistics showed that stigmastanol ferulate (VIP score = 1.22) followed by isomeric forms of kaempferol (VIP scores = 1.19) and other phenolic acids (i.e., schottenol/sitosterol ferulate and 24-methylcholestanol ferulate) were the most affected compounds through the in vitro static digestion process. The inclusion of different levels of MOLP in the recipe increased the slowly digestible starch fractions and decreased the rapidly digestible starch fractions and the starch hydrolysis index of the cooked-to-optimum samples. The present results showed that MOLP could be considered a promising ingredient in fresh pasta formulation.