The ability of populations to expand their geographic ranges, whether as invaders or climate migrants, presents among the most serious global problems today. However, fundamental mechanisms regarding factors that enable certain populations to rapidly transition to novel habitats remain poorly understood. In recent years, many species have invaded freshwater habitats from saline environments, such as the copepod Eurytemora affinis complex. We found evolutionary shifts in genome-wide in gene expression and parallel genomic signatures of selection across the saline to freshwater transition, both in wild populations and laboratory selection lines. Notably, these evolutionary changes often converged on the same ion transporters. Interestingly, we found significant correlations between acclimatory and adaptive responses in gene expression for these ion transporters. The significant plastic responses at critical loci might provide the substrate for selection during invasions. Moreover, we found significant reduction in plasticity in gene expression response at the same ion transporters in the freshwater invading populations, relative to their saline ancestors, consistent with the evolution of canalization over time. In a population genomic analysis, we found that a large portion of loci under parallel selection in the invasive populations arose from balanced polymorphisms in their native ranges (at the same SNPs within the same ion transporter paralogs!). Our findings have relevance for other invaders crossing this salinity boundary, as well as for understanding the nature of mechanisms that underlie rapid evolution during radical environmental change.