This paper develops a general framework for constructing unconditionally energy-stable exponential time differencing Runge–Kutta (ETDRK) methods for a range of gradient flows. The authors identify conditions necessary for ETDRK schemes to maintain the original energy dissipation and show that commonly used third- and fourth-order ETDRK schemes fail to meet these conditions. To address this, they introduce new third-order ETDRK schemes that satisfy the required conditions, ensuring unconditional energy decay. Extensive numerical experiments validate the accuracy, stability, and behavior of these new schemes under large time steps, long-term evolution, and adaptive time stepping across various gradient flows. This study is the first to examine unconditional energy stability for high-order ETDRK methods, and the authors are optimistic about the potential for developing even higher-order schemes.This paper develops a general framework for constructing unconditionally energy-stable exponential time differencing Runge–Kutta (ETDRK) methods for a range of gradient flows. The authors identify conditions necessary for ETDRK schemes to maintain the original energy dissipation and show that commonly used third- and fourth-order ETDRK schemes fail to meet these conditions. To address this, they introduce new third-order ETDRK schemes that satisfy the required conditions, ensuring unconditional energy decay. Extensive numerical experiments validate the accuracy, stability, and behavior of these new schemes under large time steps, long-term evolution, and adaptive time stepping across various gradient flows. This study is the first to examine unconditional energy stability for high-order ETDRK methods, and the authors are optimistic about the potential for developing even higher-order schemes.