The history of life involves countless evolutionary innovations, a steady stream of ingenuity that has been flowing for more than 3 billion years. Very little is known about the principles of biological organization that allow such innovation. Here, we examine these principles for evolutionary innovation in gene expression patterns. To this end, we study a model for the transcriptional regulation networks that are at the heart of embryonic development. A genotype corresponds to a regulatory network of a given topology, and a phenotype corresponds to a steady-state gene expression pattern. Networks with the same phenotype form a connected graph in genotype space, where two networks are immediate neighbors if they differ by one regulatory interaction. We show that an evolutionary search on this graph can reach genotypes that are as different from each other as if they were chosen at random in genotype space, allowing evolutionary access to different kinds of innovation while staying close to a viable phenotype. Thus, although robustness to mutations may hinder innovation in the short term, we conclude that long-term innovation in gene expression patterns can only emerge in the presence of the robustness caused by connected genotype graphs.