We developed an automatic slow-wave sleep (SWS) detection algorithm that can be applied to groups of healthy subjects and patients with obstructive sleep apnea (OSA). This algorithm detected SWS based on autonomic activations derived from the heart rate variations of a single sensor. An autonomic stability, which is an SWS characteristic, was evaluated and quantified using R-R intervals from an electrocardiogram (ECG). The thresholds and the heuristic rule to determine SWS were designed based on the physiological backgrounds for sleep process and distribution across the night. The automatic algorithm was evaluated based on a fivefold cross validation using data from 21 healthy subjects and 24 patients with OSA. An epoch-by-epoch (30 s) analysis showed that the overall Cohen's kappa, accuracy, sensitivity, and specificity of our method were 0.56, 89.97%, 68.71%, and 93.75%, respectively. SWS-related information, including SWS duration (min) and percentage (%), were also calculated. A significant correlation in these parameters was found between automatic and polysomnography scorings. Compared with similar methods, the proposed algorithm convincingly discriminated SWS from non-SWS. The simple method using only R-R intervals has the potential to be utilized in mobile and wearable devices that can easily measure this information. Moreover, when combined with other sleep staging methods, the proposed method is expected to be applicable to long-term sleep monitoring at home and ambulatory environments.