A common goal in the discovery of rare functional DNA variants via medical resequencing is to incur a relatively lower proportion of false positive base-calls. We developed a novel statistical method for resequencing arrays (SRMA, sequence robust multi-array analysis) to increase the accuracy of detecting rare variants and reduce the costs in subsequent sequence verifications required in medical applications. SRMA includes single and multi-array analysis and accounts for technical variables as well as the possibility of both low- and high-frequency genomic variation. The confidence of each base-call was ranked using two quality measures. In comparison to Sanger capillary sequencing, we achieved a false discovery rate of 2% (false positive rate 1.2 × 10⁻⁵, false negative rate 5%), which is similar to automated second-generation sequencing technologies. Applied to the analysis of 39 nuclear candidate genes in disorders of mitochondrial DNA (mtDNA) maintenance, we confirmed mutations in the DNA polymerase gamma POLG in positive control cases, and identified novel rare variants in previously undiagnosed cases in the mitochondrial topoisomerase TOP1MT, the mismatch repair enzyme MUTYH, and the apurinic-apyrimidinic endonuclease APEX2. Some patients carried rare heterozygous variants in several functionally interacting genes, which could indicate synergistic genetic effects in these clinically similar disorders.