Quantum critical points are characterized by scale-invariant correlations and therefore by long-range entanglement. As such, they present fascinating examples of quantum states of matter and their study is an important theme in modern physics. However, little is known about the fate of quantum criticality under non-equilibrium conditions. Here we investigate the effect of external noise sources on quantum critical points. It is natural to expect that noise will have a similar effect to finite temperature, that is, destroying the subtle correlations underlying the quantum critical behaviour. Surprisingly, we find that the ubiquitous 1/f noise does preserve the critical correlations. The emergent states show an intriguing interplay of intrinsic quantum critical and external-noise-driven fluctuations. We illustrate this general phenomenon with specific examples describing solid-state and ultracold-atoms systems. Moreover, our approach shows that genuine quantum phase transitions can exist even under non-equilibrium conditions.