Tuberculosis disease is a major global public health concern and the growing prevalence of drug-resistant Mycobacterium tuberculosis is making disease control more difficult. However, the increasing application of whole-genome sequencing as a diagnostic tool is leading to the profiling of drug resistance to inform clinical practice and treatment decision making. Computational approaches for identifying established and novel resistance-conferring mutations in genomic data include genome-wide association study (GWAS) methodologies, tests for convergent evolution and machine learning techniques. These methods may be confounded by extensive co-occurrent resistance, where statistical models for a drug include unrelated mutations known to be causing resistance to other drugs. Here, we introduce a novel 'cannibalistic' elimination algorithm ("Hungry, Hungry SNPos") that attempts to remove these co-occurrent resistant variants. Using an M. tuberculosis genomic dataset for the virulent Beijing strain-type (n = 3,574) with phenotypic resistance data across five drugs (isoniazid, rifampicin, ethambutol, pyrazinamide, and streptomycin), we demonstrate that this new approach is considerably more robust than traditional methods and detects resistance-associated variants too rare to be likely picked up by correlation-based techniques like GWAS.