Short regions of overlap between ends of antiparallel microtubules are central elements within bipolar microtubule arrays. Although their formation requires motors, recent in vitro studies demonstrated that stable overlaps cannot be generated by molecular motors alone. Motors either slide microtubules along each other until complete separation or, in the presence of opposing motors, generate oscillatory movements. Here, we show that Ase1, a member of the conserved MAP65/PRC1 family of microtubule-bundling proteins, enables the formation of stable antiparallel overlaps through adaptive braking of Kinesin-14-driven microtubule-microtubule sliding. As overlapping microtubules start to slide apart, Ase1 molecules become compacted in the shrinking overlap and the sliding velocity gradually decreases in a dose-dependent manner. Compaction is driven by moving microtubule ends that act as barriers to Ase1 diffusion. Quantitative modelling showed that the molecular off-rate of Ase1 is sufficiently low to enable persistent overlap stabilization over tens of minutes. The finding of adaptive braking demonstrates that sliding can be slowed down locally to stabilize overlaps at the centre of bipolar arrays, whereas sliding proceeds elsewhere to enable network self-organization.