<i>Pseudomonas aeruginosa</i>, a major cause of nosocomial infections, is considered a paradigm of antimicrobial resistance, largely due to hyperproduction of chromosomal cephalosporinase AmpC. Here, we explore the ability of 6-pyridylmethylidene penicillin-based sulfones <b>1-3</b> to inactivate the AmpC β-lactamase and thus rescue the activity of the antipseudomonal ceftazidime. These compounds increased the susceptibility to ceftazidime in a collection of clinical isolates and PAO1 mutant strains with different <i>ampC</i> expression levels and also improved the inhibition kinetics relative to avibactam, displaying a slow deacylation rate and involving the formation of an indolizine adduct. Bromide <b>2</b> was the inhibitor with the lowest <i>K</i><sub>I</sub> (15.6 nM) and the highest inhibitory efficiency (<i>k</i><sub>inact</sub>/<i>K</i><sub>I</sub>). Computational studies using diverse AmpC enzymes revealed that the aromatic moiety in <b>1-3</b> targets a tunnel-like site adjacent to the catalytic serine and induces the folding of the H10 helix, indicating the potential value of this not-always-evident pocket in drug design.