Abstract: Fiscal and tax incentives play an important role in stimulating technological innovation. Drawing on Punctuated Equilibrium Theory and using data from Chinese A-share listed firms during 2007—2023, this study examines how fiscal and tax policies drive Research and Development (R&D) investment to achieve a positive leap from quantitative accumulation to qualitative breakthroughs from the perspective of R&D processes and innovation modes. The results show that both fiscal subsidies and tax incentives exhibit a U-shaped effect on positive leaps in R&D investment, characterized by an initial inhibitory effect followed by a promotional effect. The interaction between the two policy instruments is significantly asymmetric: tax incentives reshape the incentive pathway of fiscal subsidies, whereas fiscal subsidies strengthen the U-shaped effect of tax incentives and raise their incentive threshold. In addition, fiscal subsidies significantly attract inflows of venture capital and private capital, while tax incentives do not generate significant spillover effects. Heterogeneity analysis indicates that the U-shaped effects are mainly observed among mature firms and large-scale enterprises. Moreover, the effect of fiscal subsidies is more pronounced in manufacturing firms, whereas the effect of tax incentives is stronger in non-manufacturing firms. Further analysis reveals that rent-seeking behavior lowers the threshold of fiscal subsidies but raises the threshold of tax incentives, while digital transformation increases the thresholds at which both policy instruments promote positive leaps in R&D investment. These findings provide empirical evidence for optimizing the design of innovation incentive policies.