We prepared a series of substituted N-(pyrazin-2-yl)benzenesulfonamides as an attempt to investigate the effect of different linkers connecting pyrazine to benzene cores on antimicrobial activity when compared to our previous compounds of amide or retro-amide linker type. Only two compounds, 4-amino-N-(pyrazin-2-yl)benzenesulfonamide (MIC = 6.25 μg/mL, 25 μM) and 4-amino-N-(6-chloropyrazin-2-yl)benzenesulfonamide (MIC = 6.25 μg/mL, 22 μM) exerted good antitubercular activity against M. tuberculosis H37Rv. However, they were excluded from the comparison as they—unlike the other compounds—possessed the pharmacophore for the inhibition of folate pathway, which was proven by docking studies. We performed target fishing, where we identified matrix metalloproteinase-8 as a promising target for our title compounds that is worth future exploration.