Frequency measurements for complex single-tone signals under additive Gaussian noise cover extensive engineering fields. Existing direct discrete Fourier transform (DFT) interpolation methods suffer both degraded accuracies under noisy conditions and biased estimation performances for a restricted number of samples. To address these problems, this article proposes a fast and accurate frequency estimation scheme using two-sample DFT interpolation. First, this work introduces a frequency deviation detector that can exactly recognize the interpolation direction. In addition, to correct the estimation biases of existing direct estimators, this article further develops an unbiased and extremely accurate estimator for an arbitrary number of samples. Finally, a fast and accurate frequency estimation scheme is proposed based on the developed detector and estimator. Results of tests indicate that the proposed scheme exhibits good noise tolerance and can provide exact bias corrections for small and medium numbers of samples. The proposed strategy can provide superior precision and serve as an efficient frequency estimation scheme in various engineering fields.