ABSTRACT We investigate the formation of dense stellar clumps in a suite of high-resolution cosmological zoom-in simulations of a massive, star-forming galaxy at z ∼ 2 under the presence of strong quasar winds. Our simulations include multiphase ISM physics from the Feedback In Realistic Environments (FIRE) project and a novel implementation of hyper-refined accretion disc winds. We show that powerful quasar winds can have a global negative impact on galaxy growth while in the strongest cases triggering the formation of an off-centre clump with stellar mass ${\rm M}_{⋆ }∼ 10^{7}\, {\rm M}_{⊙ }$, effective radius ${\rm R}_{\rm 1/2\, \rm Clump}∼ 20\, {\rm pc}$, and surface density $Σ _{⋆ } ∼ 10^{4}\, {\rm M}_{⊙ }\, {\rm pc}^{-2}$. The clump progenitor gas cloud is originally not star-forming, but strong ram pressure gradients driven by the quasar winds (orders of magnitude stronger than experienced in the absence of winds) lead to rapid compression and subsequent conversion of gas into stars at densities much higher than the average density of star-forming gas. The AGN-triggered star-forming clump reaches ${\rm SFR} ∼ 50\, {\rm M}_{⊙ }\, {\rm yr}^{-1}$ and $Σ _{\rm SFR} ∼ 10^{4}\, {\rm M}_{⊙ }\, {\rm yr}^{-1}\, {\rm kpc}^{-2}$, converting most of the progenitor gas cloud into stars in ∼2 Myr, significantly faster than its initial free-fall time and with stellar feedback unable to stop star formation. In contrast, the same gas cloud in the absence of quasar winds forms stars over a much longer period of time (∼35 Myr), at lower densities, and losing spatial coherency. The presence of young, ultra-dense, gravitationally bound stellar clumps in recently quenched galaxies could thus indicate local positive feedback acting alongside the strong negative impact of powerful quasar winds, providing a plausible formation scenario for globular clusters.