Phasing is the process of inferring haplotypes from genotype data. Efficient algorithms and associated software for accurate phasing in pedigrees are needed, especially for populations lacking reference panels of sequenced individuals. We present a novel method for phasing genotypes from whole-genome sequence data in pedigrees, called PULSAR (Phasing Using Lineage Specific Alleles/Rare variants). The method is based on the property that alleles specific to a single founding chromosome within a pedigree are highly informative for identifying haplotypes that are shared identical by descent. Simulation studies are used to assess the performance of PULSAR with various pedigree sizes and structures, and the effect of genotyping errors and the presence of nonsequenced individuals is investigated. In pedigrees with complete sequencing and realistic genotyping error rates, PULSAR correctly phases >99.9% of heterozygous genotypes, excluding sites at which all individuals are heterozygous, and does so with a switch error rate frequently below 10-4. PULSAR is highly accurate, capable of genotype error correction and imputation, and computationally competitive with alternative phasing software applicable to pedigrees. Our method has the significant advantage of not requiring reference panels that are essential for other population-based phasing algorithms. A software implementation of PULSAR is freely available.