Arterial Spin Labeled (ASL) perfusion MRI enables non-invasive, quantitative measurements of tissue perfusion, and has a broad range of applications including brain functional imaging. However, ASL suffers from low signal-to-noise ratio (SNR), limiting image resolution. Acquisitions using 3D readouts are optimal for background-suppression of static signals, but can be SAR intensive and typically suffer from through-plane blurring. In this study, we investigated the use of accelerated 3D readouts to obtain whole-brain, high-SNR ASL perfusion maps and reduce SAR deposition. Parallel imaging was implemented along the partition-encoding direction in a pseudo-continuous ASL sequence with background-suppression and 3D RARE Stack-Of-Spirals readout, and its performance was evaluated in three small cohorts. First, both non-accelerated and two-fold accelerated single-shot versions of the sequence were evaluated in healthy volunteers during a motor-photic task, and the performance was compared in terms of temporal SNR, GM-WM contrast, and statistical significance of the detected activation. Secondly, single-shot 1D-accelerated imaging was compared to a two-shot accelerated version to assess benefits of SNR and spatial resolution for applications in which temporal resolution is not paramount. Third, the efficacy of this approach in clinical populations was assessed by applying the single-shot 1D-accelerated version to a larger cohort of elderly volunteers. Accelerated data demonstrated the ability to detect functional activation at the subject level, including cerebellar activity, without loss in the perfusion signal temporal stability and the statistical power of the activations. The use of acceleration also resulted in increased GM-WM contrast, likely due to reduced through-plane partial volume effects, that were further attenuated with the use of two-shot readouts. In a clinical cohort, image quality remained excellent, and expected effects of age and sex on cerebral blood flow could be detected. The sequence is freely available upon request for academic use and could benefit a broad range of cognitive and clinical neuroscience research.