A chemically diverse set of 13 5-nitrofuran-tagged heterocyclic compounds has been prepared via the Groebke–Blackburn–Bienaymé multicomponent reaction. The testing of these compounds against the so-called ESKAPE panel of pathogens identified an apparent lead compound—N-cyclohexyl-2-(5-nitrofuran-2-yl)imidazo[1,2-a]pyridine-3-amine (4a)—which showed an excellent profile against Enterobacter cloacae, Staphylococcus aureus, Klebsiella pneumoniae, and Enterococcus faecalis (MIC 0.25, 0.06, 0.25 and 0.25 µg/mL, respectively). Its antibacterial profile and practically convenient synthesis warrant further pre-clinical development. Certain structure-activity relationships were established in the course of this study which were rationalized by the flexible docking experiments in silico. The assessment of antitubercular potential of the compounds synthesized against drug sensitive H37v strain of Mycobacterium tuberculosis revealed little potential of the imidazo-fused products of the Groebke–Blackburn–Bienaymé multicomponent reaction as chemotherapeutic agents against this pathogen.