Three-dimensional (3D) particle focusing in microfluidics is a fundamental capability with a wide range of applications, such as on-chip flow cytometry, where high-throughput analysis at the single-cell level is performed. Currently, 3D focusing is achieved mainly in devices with complex layouts, additional sheath fluids, and complex pumping systems. In this work, we present a compact microfluidic device capable of 3D particle focusing at high flow rates and with a small footprint, without the requirement of external fields or lateral sheath flows, but using only a single-inlet, single-outlet microfluidic sequence of straight channels and tightly curving vertical loops. This device exploits inertial fluidic effects that occur in a laminar regime at sufficiently high flow rates, manipulating the particle positions by the combination of inertial lift forces and Dean drag forces. The device is fabricated by femtosecond laser irradiation followed by chemical etching, which is a simple two-step process enabling the creation of 3D microfluidic networks in fused silica glass substrates. The use of tightly curving three-dimensional microfluidic loops produces strong Dean drag forces along the whole loop but also induces an asymmetric Dean flow decay in the subsequent straight channel, thus producing rapid cross-sectional mixing flows that assist with 3D particle focusing. The use of out-of-plane loops favors a compact parallelization of multiple focusing channels, allowing one to process large amounts of samples. In addition, the low fluidic resistance of the channel network is compatible with vacuum driven flows. The resulting device is quite interesting for high-throughput on-chip flow cytometry.