The analysis of the temporal dynamics in intrapartum fetal heart rate (FHR), aiming at early detection of fetal acidosis, constitutes an intricate signal processing task, that continuously receives significant research efforts. Entropy and entropy rates, envisaged as measures of complexity, often computed via popular implementations referred to as Approximate Entropy (ApEn) or Sample Entropy (SampEn), have regularly been reported as significant features for intrapartum FHR analysis. The present contribution aims to show how mutual information enhances characterization of FHR temporal dynamics and improves fetal acidosis detection performance. To that end, mutual information is first connected to ApEn and SampEn both conceptually and with respect to estimation procedure. Second, mutual information, ApEn and SampEn are computed on a large (≃ 1000 subjects) and documented database of FHR data, collected in a French academic hospital. Reported results show that the use of mutual information permits to significantly outperform ApEn and SampEn for acidosis detection, during any stage of labor.