Scientific and technological frontiers advance through punctuated dynamics, yet the principles governing these dynamics remain poorly understood. Here we collect and analyze datasets tracking the evolution of frontiers across 9 different domains, spanning materials discovery, structural biology, AI, computational biomedicine, data science, theoretical computer science, Formula-1 racing, and physical wheel building. Analyzing 6.8M solutions to 6.7K tasks, we uncover three universal patterns: (1) waiting times between new frontiers are heavy-tailed, with most attempts concentrated in long stasis; (2) frontier records accumulate at a sublinear rate, faster than logarithmic yet slower than linear growth; (3) record-breaking events are temporally correlated, generating short-term predictability yet long-term unpredictability. Despite the differences in the scale, scope, and definition of the settings, these patterns are remarkably consistent across all domains we study, and are not captured by models from complex systems, record statistics, economics of innovation, and cultural evolution. We trace the missing ingredient to the distinction between radical and incremental innovation, and develop a minimal, analytically solvable model incorporating both radical resets that restructure what is achievable and incremental refinements that exploit the current frontier. The simple model reproduces all three empirical regularities. Remarkably, the leading-order predictions are parameter-independent, identifying a new universality class governing punctuated progress and yielding testable predictions about how openness and access to frontier solutions shape the pace of advance. Overall, these results reveal universal dynamics governing punctuated progress and identify the interplay between radical resets and incremental refinements as the key driver of how scientific and technological frontiers advance.