I expect this information is reasonably well documented in histories of particular currents of thought. I have no idea how often it happens in absolute terms, but I feel it must be relatively common because I have encountered it as an amateur reader of papers.
A good example is ET Jaynes' work on maximum caliber, which is a variational principle for dynamical systems. It might be cheating because it is well-understood to be a controversial concept, but the insights concerned entropy. Jaynes' specialty was Statistical Mechanics, for which he had employed information-theoretic notions of entropy in order to account for the lack of knowledge of the microstates. When Jaynes' was writing, physics used the Clausius formulation of 2nd Law of Thermodynamics, which he found unsatisfactory for the problem of prediction because it says nothing about intermediate states before reaching equilibrium. In Physical Chemistry they used a different one, which came from work by G.N. Lewis, who used the Gibbs formulation of the 2nd Law. It is insights drawn from the subtleties of Gibbs' work concerning entropy that gave Jaynes the predictive power he was interested in. Lastly, Jaynes had the work of Clifford Truesdell who was writing around the same time in the field of Continuum Mechanics, and working to expand that approach to fully cover thermodynamics. Truesdell's work persuaded Jaynes that the other approaches were in fact wrong.
So here was a case where one physics researcher (Jaynes) borrowed math ideas from communication (Shannon), then read older work from chemistry (Lewis), leading to much older work in early thermodynamics that had new insights (Gibbs), and confirmed by more recent work in a different field of math (Truesdell). All of these insights went into his work on maximum caliber.
In a similar vein, a lot of Truesdell's writing consists of going back to the early days of thermodynamics and finely sifting the insights therein. He writes well and carefully, but is animated and polemical; I recommend reading him to anyone interested in thermodynamics.