I present a recent historical case from cosmology-the story of inflationary cosmology-and on its basis argue that solving explanatory problems is a reliable method for making progress in science. In particular, I claim that the success of inflationary theory at solving its predecessor's explanatory problems justified the theory epistemically, even in advance of the development of novel predictions from the theory and the later confirmation of those predictions. 1Introduction2A Portrait of the Argument as a Short Précis3A Brief History of Inflationary Theory4Empiricist Interpretations of Inflationary Case5A Confutation of Empiricist Interpretations6Explanationist Interpretation of Inflationary Case7Concluding Remarks.