Nanofluidic devices make use of molecular-level forces and phenomena to increase their density, speed and accuracy. However, fabrication is challenging, because dissimilar materials need to be integrated in three dimensions with nanoscale precision. Here, we report a three-dimensional nanoscale liquid glass electrode made from monolithic substrates without conductive materials by femtosecond-laser nanomachining. The electrode consists of a nanochannel terminating at a nanoscale glass tip that becomes a conductor in the presence of high electric fields through dielectric breakdown, and returns to being an insulator when this field is removed. This reversibility relies on control of nanoampere breakdown currents and extremely fast heat dissipation at nanoscale volumes. We use the nanoscale liquid glass electrode to fabricate a nano-injector that includes an electrokinetic pump, 4 microm across with 0.6 microm channels, which is capable of producing well-controlled flow rates below 1 fl s(-1). The electrode can be integrated easily into other nanodevices and fluidic systems, including actuators and sensors.