(1) Background: Epidural analgesia (EA), at the present time, is one of the most effective methods to reduce labor pain. In recent years its use has increased, being used between 20–70% of all deliveries; (2) Methods: Historical cohort on a total of 2947 deliveries during the years 2012–2016 at the “Mancha-Centro Hospital” of Alcázar de San Juan. The main outcome variables were four neonatal morbidity (NM) criteria: umbilical artery pH of <7.10, Apgar score at 5 min < 7, need for advanced resuscitation and composite morbidity. We used the multivariate analysis to control confounding bias. (3) Results: No statistical relationship between EA and the second stage of labor duration with none of the four criteria of NM used (p > 0.005). However, the type of delivery was associated with three criteria (pH, resuscitation, and composite morbidity). The instrumental delivery presented an OR of pH < 7.10 of 2.68 95% CI [1.15, 6.27], an OR of advanced resuscitation of 2.44 95% CI [1.17, 5.08] and OR of composite morbidity of 2.86 95% CI [1.59, 5.12]; (4) Conclusions: The EA and the second stage of labor duration are not related to the NM. While the instrumental delivery doubles the risk of NM compared to the normal vaginal delivery.