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We present a novel MFCC-based scheme for the Bandwidth Extension (BWE) of narrowband speech. BWE is based on the assumption that narrowband speech (0.3.3.4 kHz) correlates closely with the highband signal (3.4.7 kHz), enabling estimation of the highband frequency content given the narrow band. While BWE schemes have traditionally used LP-based parametrizations, our recent work has shown that MFCC parametrization results in higher correlation between both bands reaching twice that using LSFs. By employing high-resolution IDCT of highband MFCCs obtained from narrowband MFCCs by statistical estimation, we achieve high-quality highband power spectra from which the time-domain speech signal can be reconstructed. Implementing this scheme for BWE translates the higher correlation advantage of MFCCs into BWE performance superior to that obtained using LSFs, as shown by improvements in log-spectral distortion as well as Itakura-based measures (the latter improving by up to 13%).