This study evaluated the antibacterial efficacy of methanolic extracts of isolated endophytic fungi from stem barks and leaves of Alstonia boonei De Wild and Greenwayodendron suaveolens (Engl. and Diels) Verdc. subsp. Suaveolens against Klebsiella pneumoniae ATCC 43816, Haemophilus influenzae ATCC 49247, Pseudomonas aeruginosa ATCC 27853, and Escherichia coli ATCC 35218, responsible for causing pneumonia. The endophytic fungi were isolated and characterized in the Potato Dextrose Agar (PDA), Sabouraud Dextrose Agar (SDA), and Czapek Dox Agar (CDA) media. The fungi and their methanolic extracts were tested for in vitro antibacterial potential by antagonistic assay for endophytic fungi against bacterial pathogens and microdilution method. The phytochemical screening of extracts was carried out according to the colorimetric and precipitation methods to reveal the presence of secondary metabolites. The results showed that 24 macroscopically and microscopically distinct endophytic fungi were isolated, identified, and stored. These endophytic fungi possessed antibacterial activity against the selected bacterial strains with inhibition zones ranging from 7.00 to 25.00 mm. The endophytic fungi GS15 and AB24 have presented the inhibitions zones of 20.33 mm and 25.00 mm, respectively, and these were better than the ones obtained for Levofloxacin®. The endophytes with inhibition zones greater than 10 mm were used for extraction of their secondary metabolites. The endophytic fungi extracts showed antibacterial activity with the minimum inhibitory concentrations (MICs) ranging from 6.25 × 10$^{−4}$ to 2 × 10$^{−2}$ g/L and the minimum bactericidal concentrations (MBCs) ranging from 2.5 × 10$^{−3}$ to 2 × 10$^{−2}$ g/L. The endophytic fungi GS15 extract was the most effective extract; it showed bactericidal effects on the tested bacterial strains. The phytochemical screening of the extracts revealed the presence of secondary metabolites classes, responsible for causing the obtained antibacterial activity. Thus, the endophytic fungi methanolic extracts from A. boonei and G. suaveolens have the potential to inhibit the growth of bacteria responsible for nosocomial pneumonia.