This paper proposes a super-resolution direction-of-arrival (DOA) estimator using coprime sensor arrays (CSAs) with the min processor. The min processor resolves the CSA subarrays' spatial aliasing while achieving lower sidelobes than the product processor and maintaining a positive semi-definite spatial power spectral density (PSD) estimation. The spatial correlation function implied by the CSAmin PSD populates a Hermitian Toeplitz augmented covariance matrix, which MUSIC processes to estimate the source DOAs. The proposed algorithm outperforms previously proposed coprime MUSIC DOA estimation from spatial smoothing of pairwise sensor correlation estimates in scenarios with few snapshots and a wide dynamic range of source powers.