Shaping electron beams with cycles of light provides femtosecond and attosecond time resolution in electron microscopy and enables fundamental quantum-coherent measurements. However, efficient light-electron control requires a prolonged interaction between the two beams for cascaded transfer of photon energy and momentum to the freely propagating electrons. Here we report the use of traveling evanescent terahertz waves to achieve velocity matching and thereby high acceleration gradients both in space and in time. With experiment and simulations, we demonstrate attosecond streaking, temporal pulse compression, acceleration, and spatial focusing of subrelativistic electron pulses with a single evanescent-wave element under the control of selected terahertz delays and phases. Based on these results, we propose to use a symmetric arrangement with two evanescent terahertz waves to generate isolated attosecond electron pulses in a beam with realistic parameters. These results establish subluminal terahertz waves as a promising tool for ultrafast electron pulse control.