Mechanistic studies of animal and plant motion often focus on the fundamental units of biological actuation: individual motor cells. Recent advances spanning the fields of muscle physiology and biomimetic actuation, however, reveal that important mechanical behaviors also arise at higher levels of organization, driven by the interplay of motor cells with connective tissue networks that guide and control en masse deformation. Here we illustrate how a paradigm of cell-driven actuation augmented by a mechanically crucial extracellular matrix is equally applicable to plant pulvini; motor organs evolutionarily distinct from but mechanically analogous to animal muscles. Using pulvini from the sensitive plant Mimosa pudica, we visualized anatomical sources of mechanical anisotropy at three hierarchical scales of pulvinus organization, built hydraulic physical models of observed morphologies, and analyzed 3D changes in the shapes of osmotically pressurized pulvini. We find that extracellular guidance controls the direction and extent of turgor-induced pulvinus deformation, an effect that ultimately influences the magnitude, speed, and energetic cost of pulvinus-driven motion. We discuss the relevance of these findings to ongoing work in the fields of muscle physiology and soft robotics, and we situate pulvini within a conceptual framework for understanding the design of biological motor organs generally.