Hybridization and gene flow between species appears to be common. Even though it is clear that hybridization is widespread across all surveyed taxonomic groups, the magnitude and consequences of introgression are still largely unknown. Thus it is crucial to develop the statistical machinery required to uncover which genomic regions have recently acquired haplotypes via introgression from a sister population. We developed a novel machine learning framework, called FILET (Finding Introgressed Loci via Extra-Trees) capable of revealing genomic introgression with far greater power than competing methods. FILET works by combining information from a number of population genetic summary statistics, including several new statistics that we introduce, that capture patterns of variation across two populations. We show that FILET is able to identify loci that have experienced gene flow between related species with high accuracy, and in most situations can correctly infer which population was the donor and which was the recipient. Here we describe a data set of outbred diploid Drosophila sechellia genomes, and combine them with data from D. simulans to examine recent introgression between these species using FILET. Although we find that these populations may have split more recently than previously appreciated, FILET confirms that there has indeed been appreciable recent introgression (some of which might have been adaptive) between these species, and reveals that this gene flow is primarily in the direction of D. simulans to D. sechellia.