The estimation of ground-state and thermal equilibrium properties of quantum many-body systems is an important but challenging problem in the simulation of quantum physics. In computational physics, imaginary time evolution (ITE) is a key ingredient in many algorithms for computing such properties. However, performing ITE with general quantum many-body Hamiltonians on classical computers is computationally difficult. A number of quantum algorithms have been developed for ITE, including recent proposals [1] that are aimed at intermediate to near-term quantum computers. Nevertheless, implementing these algorithms on hardware is likely to require extensive error-mitigation. In this work, we propose a new quantum algorithm to compute imaginary-time evolved expectation values which incorporates ideas from quantum error-mitigation [2]. Specifically, we use a technique inspired by probabilistic error-cancellation (PEC) [2] to efficiently implement a trotterized ITE as a probabilistic linear combination of quantum circuits followed by post-processing. Our algorithm for ITE is inherently noise-resilient since we can directly implement it as a probabilistic linear combination of native noisy gates. Our method is especially well-suited to estimating thermal expectation values using the so-called thermal pure quantum (TPQ) states [3], which can be prepared from simple start states using ITE. We demonstrate our algorithm for ITE by performing numerical (classical) simulations and by implementing it on an IBM quantum computer (see Fig. 1). The agreement of the experimental data with the theoretical value demonstrates the noise-resilience of our algorithm. In our work, we also analyze our ITE algorithm as applied to the preparation of TPQ states and classically simulate it to prepare TPQ states of the 1D Heisenberg Hamiltonian for up to 7 qubits.