Heavy element accumulation and stellar mass assembly are fundamental processes in the formation and evolution of galaxies. However, the key elements that govern them, such as gas accretion and outflow, are not fully understood. This is especially true for luminous and massive galaxies, which usually suffer strong feedback as massive outflows and large-scale gas accretion triggered by galaxy interactions. Using a sample of 77 luminous infrared (IR) galaxies, we derive chemical abundances using new diagnostics based on nebular IR lines, which peer through their dusty medium and allow us to include the obscured metals. In contrast to optically based studies, our analysis reveals that most luminous IR galaxies remain close to the mass-metallicity relation. Four galaxies with extreme star formation rates (>60M_{sun}_/yr) in their late-merger stages show strongly depressed metallicities (12+log(O/H)~7.7-8.1) along with solar-like N/O ratios, indicative of gas mixing processes and suggesting the action of massive infall of metal-poor gas in a short phase, eventually followed by rapid enrichment. These results challenge the classical gas equilibrium scenario applied to main-sequence galaxies, suggesting that chemical enrichment and stellar-mass growth in luminous IR galaxies likely occur via mergers, driving these galaxies out of chemical equilibrium.