The high temporal and intensity resolution of modern accelerometers gives the opportunity of detecting even tiny body movements via motion-based sensors. In this paper, we demonstrate and evaluate an approach to identify pulse waves and heartbeats from acceleration data of the human wrist during sleep. Specifically, we have recorded simultaneously full-night polysomnography and 3d wrist actigraphy data of 363 subjects during one night in a clinical sleep laboratory. The acceleration data was segmented and cleaned, excluding body movements and separating episodes with different sleep positions. Then, we applied a bandpass filter and a Hilbert transform to uncover the pulse wave signal, which worked well for an average duration of 1.7 h per subject. We found that 81 percent of the detected pulse wave intervals could be correctly associated with the R peak intervals from independently recorded ECGs and obtained a median Pearson cross-correlation of 0.94. While the low-frequency components of both signals were practically identical, the high-frequency component of the pulse wave interval time series was increased, indicating a respiratory modulation of pulse transit times, probably as an additional contribution to respiratory sinus arrhythmia. Our approach could be used to obtain long-term nocturnal heartbeat interval time series and pulse wave signals from wrist-worn accelerometers without the need of recording ECG or photoplethysmography. This is particularly useful for an ambulatory monitoring of high-risk cardiac patients as well as for assessing cardiac dynamics in large cohort studies solely with accelerometer devices that are already used for activity tracking and sleep pattern analysis.