Provided are a computer program product, system, and method for replicating a source data set to a target data store. A point-in-time copy of the source data set is generated having a data structure identifying the data in the source data set as of a point-in-time. A restore operation is initiated to copy the source data set represented by the point-in-time copy to a restored copy of the source data set consistent with the source data set. The source data set records are transferred from the restored copy to the target data store in the target storage.