Domain integration remains a limiting factor in Galerkin-based numerical methods, particularly when advanced approximations such as meshfree methods, generalized partition of unity methods, and convolution-based finite element methods are employed. Stabilized conforming nodal integration (SCNI) introduces smoothed gradients over conforming nodal subdomains to recover Galerkin exactness and establishes the concept of integration constraint [1]. Subsequently, the variationally consistent integration method generalized this idea by satisfying integration constraints through appropriate modifications of the test functions [2]. Motivated by these developments, a gradient-smoothed nodal integration is introduced, based on non-confirming nodal subdomains for gradient smoothing [3], thereby distinguishing it from the SCNI. The proposed method achieves linear exactness without non-confirming cells and, under certain conditions, quadratic exactness without additional computational cost. Convergence properties for partial differential equations with various boundary conditions are analyzed and verified through numerical examples. Furthermore, the proposed nodal integration scheme is extended to the semi-Lagrangian framework for large deformation problems. Benchmark problems are presented to demonstrate the accuracy, robustness, and computational advantages of the proposed approach.