The quantitation of rare somatic mutations is essential for basic research and translational clinical applications including minimal residual disease (MRD) detection. Though unique molecular identifier (UMI) has suppressed sequencing error and allowed detection rare mutation, the sequencing depth requirement is high. The blocker displacement amplification (BDA) allele enrichment method allows detection of rare mutations using low sequencing depth, but requires calibration to accurately quantitate the VAF of novel mutations. Here, we present Quantitative Blocker Displacement Amplification (QBDA), a method that allows accurate detection and quantitation of mutations below 0.01% VAF at only 23,000X depth. QBDA integrates sequence-selective variant enrichment into UMI quantitation allowing confident detection of rare mutations and reduced sequencing depth. Using a panel of 20 genes recurrently altered in acute myeloid leukemia, we demonstrate quantitation of various mutations including single base substitutions and indels down to a VAF of 0.001% at a single locus with less than 4 million sequencing reads, allowing a sensitive minimal residual disease (MRD) detection in patients during complete remission. In a comprehensive pan-cancer panel covering 61 genes and a melanoma hotspot panel covering 8 genes, we detect mutations down to 0.1% VAF using only 1 million reads in a broad range of clinical samples including cell-free DNA and FFPE DNA, enabling tissue or liquid biopsy genetic tests with de-centralized sequencing instruments. QBDA thus provides a convenient and versatile method for sensitive mutation quantitation using low-depth sequencing.