Coordination in groups faces a sub-optimization problem and theory suggests that some randomness may help to achieve global optima. Here we performed experiments involving a networked colour coordination game in which groups of humans interacted with autonomous software agents (known as bots). Subjects (n = 4,000) were embedded in networks (n = 230) of 20 nodes, to which we sometimes added 3 bots. The bots were programmed with varying levels of behavioural randomness and different geodesic locations. We show that bots acting with small levels of random noise and placed in central locations meaningfully improve the collective performance of human groups, accelerating the median solution time by 55.6%. This is especially the case when the coordination problem is hard. Behavioural randomness worked not only by making the task of humans to whom the bots were connected easier, but also by affecting the gameplay of the humans among themselves and hence creating further cascades of benefit in global coordination in these heterogeneous systems.