Although second-generation HIV integrase strand-transfer inhibitors (INSTIs) are prescribed throughout the world, the mechanistic basis for the superiority of these drugs is poorly understood. We used single-particle cryo-electron microscopy to visualize the mode of action of the advanced INSTIs dolutegravir and bictegravir at near-atomic resolution. Glutamine-148 -> histidine (Q148H) and glycine-140 -> serine (G140S) amino acid substitutions in integrase that result in clinical INSTI failure perturb optimal magnesium ion coordination in the enzyme active site. The expanded chemical scaffolds of second-generation compounds mediate interactions with the protein backbone that are critical for antagonizing viruses containing the Q148H and G140S mutations. Our results reveal that binding to magnesium ions underpins a fundamental weakness of the INSTI pharmacophore that is exploited by the virus to engender resistance and provide a structural framework for the development of this class of anti-HIV/AIDS therapeutics.