Monilinia laxa causes serious postharvest damage on apricot fruits under shelf-life storage conditions. Plant elicitors of methyl jasmonate (MeJA) and salicylic acid (SA) can reduce this damage, and their research can explain the background of the plant defense physiological processes in M. laxa-infected fruits. The aims of this study were: (i) to evaluate the effect of various concentrations of MeJA and SA on brown rot incidence (BRI) and lesion diameter (LD) of apricot fruits; (ii) to measure the temporal patterns for the effect of 0.4 mmol L−1 MeJA and 2 mmol L−1 SA treatments on BRI, LD and seven fruit measures (fruit firmness (FF), lignin content (LC), total soluble phenol content (TSPC), total antioxidant capacity (TAC) and enzyme activities of PAL, POD and SOD) in treatments of M. laxa-inoculated versus (vs.) non-inoculated fruits over an eight-day shelf-life storage period; and (iii) to determine inter-correlations among the seven fruit measures for MeJA and SA treatments. Both MeJA and SA significantly reduced BRI and LD. LC, FF, TAC, TSPC, as well as SOD and PAL activities in the MeJA and SA treatments were higher than the water-treated control in most assessment days and both inoculation treatments. In both inoculation treatments, the activity of POD in the SA-treated fruits was higher than MeJA-treated and control fruits at all dates. In MeJA vs. SA and inoculated vs. non-inoculated treatments, six variable pairs (FF vs. TSPC, FF vs. TAC, TAC vs. PAL, PAL vs. POD, PAL vs. SOD, and POD vs. SOD) showed significant inter-correlation values. Principal component analyses explained 96% and 93% of the total variance for inoculated and non-inoculated treatments, respectively. In inoculated treatments, both PC1 and PC2 explained 41% of the total variance and correlated with FF, TSPC and TAC and with PAL, SOD and POD, respectively. In non-inoculated treatments, PC1 and PC2 explained 49% and 44% of the total variance and correlated with LC, PAL, POD and SOD and with FF, TSPC and TAC, respectively. It can be concluded that MeJA and SA are useful in the practice to enhance the plant defense system against brown rot by reducing fungal growth and by improving physical and antioxidant attributes (FF, LC, TAC and TSPC) and the activity of defense-related enzymes (PAL, POD and SOD) in apricot fruits during shelf-life storage conditions.