Bulk-metallic glasses (BMGs) are now candidate materials for structural applications due to their exceptional strength and toughness. However, their fatigue resistance can be poor and inconsistent, severely limiting their potential as reliable structural materials. As fatigue limits are invariably governed by the local arrest of microscopically small cracks at microstructural features, the lack of microstructure in monolithic glasses, often coupled with other factors, such as the ease of crack formation in shear bands or a high susceptibility to corrosion, can lead to low fatigue limits (some ∼1/20 of their tensile strengths) and highly variable fatigue lives. BMG-matrix composites can provide a solution here as their duplex microstructures can arrest shear bands at a second phase to prevent cracks from exceeding critical size; under these conditions, fatigue limits become comparable with those of crystalline alloys. Here, we report on a Pd-based glass that similarly has high fatigue resistance but without a second phase. This monolithic glass displays high intrinsic toughness from extensive shear-band proliferation with cavitation and cracking effectively obstructed. We find that this property can further promote fatigue resistance through extrinsic crack-tip shielding, a mechanism well known in crystalline metals but not previously reported in BMGs, whereby cyclically loaded cracks propagate in a highly "zig-zag" manner, creating a rough "staircase-like" profile. The resulting crack-surface contact (roughness-induced crack closure) elevates fatigue properties to those comparable to crystalline alloys, and the accompanying plasticity helps to reduce flaw sensitivity in the glass, thereby promoting structural reliability.