We present a sampling-based control approach that can generate smooth actions for general nonlinear systems without external smoothing algorithms. Model Predictive Path Integral (MPPI) control has been utilized in numerous robotic applications due to its appealing characteristics to solve non-convex optimization problems. However, the stochastic nature of sampling-based methods can cause significant chattering in the resulting commands. Chattering becomes more prominent in cases where the environment changes rapidly, possibly even causing the MPPI to diverge. To address this issue, we propose a method that seamlessly combines MPPI with an input-lifting strategy. In addition, we introduce a new action cost to smooth control sequence during trajectory rollouts while preserving the information theoretic interpretation of MPPI, which was derived from non-affine dynamics. We validate our method in two nonlinear control tasks with neural network dynamics: a pendulum swing-up task and a challenging autonomous driving task. The experimental results demonstrate that our method outperforms the MPPI baselines with additionally applied smoothing algorithms.