Viruses diversify over time within hosts, often undercutting the effectiveness of host defenses and therapeutic interventions. To design successful vaccines and therapeutics, it is critical to better understand viral diversification, including comprehensively characterizing the genetic variants in viral intra-host populations and modeling changes from transmission through the course of infection. Massively parallel sequencing technologies can overcome the cost constraints of older sequencing methods and obtain the high sequence coverage needed to detect rare genetic variants (< 1%) within an infected host, and to assay variants without prior knowledge. Critical to interpreting deep sequence data sets is the ability to distinguish biological variants from process errors with high sensitivity and specificity. To address this challenge, we describe V-Phaser, an algorithm able to recognize rare biological variants in mixed populations. V-Phaser uses covariation (i.e. phasing) between observed variants to increase sensitivity and an expectation maximization algorithm that iteratively recalibrates base quality scores to increase specificity. Overall, V-Phaser achieved > 97% sensitivity and > 97% specificity on control read sets. On data derived from a patient after four years of HIV-1 infection, V-Phaser detected 2,015 variants across the -10 kb genome, including 603 rare variants (< 1% frequency) detected only using phase information. V-Phaser identified variants at frequencies down to 0.2%, comparable to the detection threshold of allele-specific PCR, a method that requires prior knowledge of the variants. The high sensitivity and specificity of V-Phaser enables identifying and tracking changes in low frequency variants in mixed populations such as RNA viruses.