Stimulus-responsive (SR), solvated polymers can switch between an expanded state and a collapsed state via external stimuli. Using molecular dynamics simulations, I show that such SR polymers can be employed to control the frictional response between two opposing polymer brushes in relative sliding motion. By using a brush composed of SR polymers in contact with a nonresponding solvated polymer brush, the presence of capillaries and the overlap between molecules of the opposing brushes can be switched. When both brushes are solvated, a capillary is formed and polymers of the opposing brushes interdigitate. Interdigitation dominates friction upon shearing flat brush-bearing surfaces, while the breaking and formation of capillaries dominate friction in the low-velocity limit between rough brush-bearing surfaces. Thus, when either rough or flat polymer-bearing surfaces are sheared, friction between two swollen brushes can be high. In contrast, when the SR brush is collapsed, the solvent absorbs only in the brush that does not respond to the external stimulus. The latter circumvents the presence of capillaries and interdigitation of the brushes, which results in a low friction force upon shearing.