Technological knowledge plays an important role in shaping regional economic performance. This study examines the relationship between the sophistication of regional technological capabilities and economic growth across Japanese prefectures. Using approximately 3.9 million corporate patent records filed from fiscal years 1981 to 2015, we construct bipartite networks linking 47 prefectures to 35 technology classes and apply the Fitness-Complexity algorithm to derive regional Fitness scores for seven five-year periods. We estimate fixed-effects panel models with Driscoll-Kraay standard errors, using the annual average growth rate of real gross regional product per capita over the subsequent five years as the dependent variable. Prefectural Fitness is positively associated with subsequent growth ($\hatβ = 0.0029$, $p = 0.007$) after controlling for initial income, population density, and patenting activity, but this relationship is detectable only when both entity and time fixed effects are included. Cross-sectional correlations between Fitness and subsequent growth change sign across periods, underscoring the importance of the panel approach. The growth effect of Fitness is stronger in prefectures with lower initial income, suggesting that technological sophistication contributes more to growth where there is greater scope for economic expansion. Lag and lead analyses indicate that the relationship runs from Fitness to subsequent growth rather than the reverse.