Network controllability is a powerful tool to study the causal relationships in complex systems and identify the driver nodes for steering the network dynamics into desired states. However, due to ill-posed conditions, results become unreliable when the number of drivers becomes too small compared to the network size. This is a very common situation, particularly in real-world applications, where the possibility to access multiple nodes at the same time is limited by technological constraints, such as in the human brain. Although targeting small network parts might improve accuracy in general, challenges may still remain for extremely unbalanced situations, when for example there is one single driver. To address this problem, we developed a mathematical framework that combines concepts from spectral graph theory and output controllability. Instead of controlling the original network dynamics, we aimed to control its low-dimensional embedding into the topological space derived from the Laplacian network structure. By performing extensive simulations on synthetic networks, we showed that a relatively low number of projected components is enough to improve the overall control accuracy, notably when dealing with very few drivers. Based on these findings, we introduced alternative lowdimensional controllability metrics and used them to identify the main driver areas of the human connectome obtained from N=6134 healthy individuals in the UK-biobank cohort. Results revealed previously unappreciated influential regions compared to standard controllability approaches, enabled to draw control maps between distinct specialized large-scale brain systems, and yielded an anatomically-based understanding of cerebral specialization. Taken together, our results offered a theoretically-grounded solution to deal with network controllability in real-life applications and provided insights into the causal interactions of the human brain.