The threat to public health resulting from the emergence of antimicrobial resistance (AMR) is ever rising. One of the major bacterial pathogens at the forefront of this problem is methicillin-resistant Staphylococcus aureus, or MRSA, for which there is a great need to find alternative treatments. One of the most promising alternatives is endophytic fungi, which were shown to produce a vast array of bioactive compounds, including many novel antibacterial compounds. In this study, two endophytic Alternaria sp., EL 24 and EL 35, were identified from the leaves of Eremophila longifolia. Ethyl acetate (EtOAc) extracts of their culture filtrates were found to inhibit both methicillin-sensitive S. aureus ATCC 25923 and MRSA strains M173525 and M180920. The activity of each extract was shown to be greatly affected by the growth medium, with considerable reductions in minimum inhibitory concentrations (MICs) and minimum bactericidal concentrations (MBCs) observed when tested in tryptic soy broth with glucose (TSBG) compared with Mueller–Hinton broth (MHB). Both extracts displayed significant (p ≤ 0.05) antibiofilm activity against all three S. aureus strains, the greatest of which was that of EL 35, which reduced biofilm formation by M180920 by 72%, while that of EL 24 resulted in a 57% reduction against ATCC 25923. Both extracts also disrupted established biofilms, of which the most effective was EL 35, which reduced the M180920 biofilm by 64%, while EL 24 also performed best against M180920, reducing biofilm by 54%. Gas chromatography–mass spectrometry (GC-MS) analysis of the EL 24 EtOAc extract revealed five known compounds. This study highlights the promise of endophytic fungi from Australian plants as a potential source of substances effective against important bacterial pathogens. Further understanding of the responsible compounds and their mechanisms could lead to the development of treatments effective against MRSA, as well as novel biofilm-resistant biomedical materials, contributing towards reducing the burden of AMR.