We propose a new and simple strategy for controlled ionization-induced trapping of electrons in a beam-driven plasma accelerator. The presented method directly exploits electric wakefields to ionize electrons from a dopant gas and capture them into a well-defined volume of the accelerating and focusing wake phase, leading to high-quality witness bunches. This injection principle is explained by example of three-dimensional particle-in-cell calculations using the code OSIRIS. In these simulations a high-current-density electron-beam driver excites plasma waves in the blowout regime inside a fully ionized hydrogen plasma of density 5×10(17)cm-3. Within an embedded 100 μm long plasma column contaminated with neutral helium gas, the wakefields trigger ionization, trapping of a defined fraction of the released electrons, and subsequent acceleration. The hereby generated electron beam features a 1.5 kA peak current, 1.5 μm transverse normalized emittance, an uncorrelated energy spread of 0.3% on a GeV-energy scale, and few femtosecond bunch length.