Accurate replication of DNA requires stringent regulation to ensure genome integrity. In human cells, thousands of origins of replication are coordinately activated during S phase, and the velocity of replication forks is adjusted to fully replicate DNA in pace with the cell cycle1. Replication stress induces fork stalling and fuels genome instability2. The mechanistic basis of replication stress remains poorly understood despite its emerging role in promoting cancer2. Here we show that inhibition of poly(ADP-ribose) polymerase (PARP) increases the speed of fork elongation and does not cause fork stalling, which is in contrast to the accepted model in which inhibitors of PARP induce fork stalling and collapse3. Aberrant acceleration of fork progression by 40% above the normal velocity leads to DNA damage. Depletion of the treslin or MTBP proteins, which are involved in origin firing, also increases fork speed above the tolerated threshold, and induces the DNA damage response pathway. Mechanistically, we show that poly(ADP-ribosyl)ation (PARylation) and the PCNA interactor p21Cip1 (p21) are crucial modulators of fork progression. PARylation and p21 act as suppressors of fork speed in a coordinated regulatory network that is orchestrated by the PARP1 and p53 proteins. Moreover, at the fork level, PARylation acts as a sensor of replication stress. During PARP inhibition, DNA lesions that induce fork arrest and are normally resolved or repaired remain unrecognized by the replication machinery. Conceptually, our results show that accelerated replication fork progression represents a general mechanism that triggers replication stress and the DNA damage response. Our findings contribute to a better understanding of the mechanism of fork speed control, with implications for genomic (in)stability and rational cancer treatment.