Precise control of the electronic surface states of two-dimensional (2D) materials could improve their versatility and widen their applicability in electronics and sensing. To this end, chemical surface functionalization has been used to adjust the electronic properties of 2D materials. So far, however, chemical functionalization has relied on lattice defects and physisorption methods that inevitably modify the topological characteristics of the atomic layers. Here we make use of the lone pair electrons found in most of 2D metal chalcogenides and report a functionalization method via a Lewis acid-base reaction that does not alter the host structure. Atomic layers of n-type InSe react with Ti(4+) to form planar p-type [Ti(4+)n(InSe)] coordination complexes. Using this strategy, we fabricate planar p-n junctions on 2D InSe with improved rectification and photovoltaic properties, without requiring heterostructure growth procedures or device fabrication processes. We also show that this functionalization approach works with other Lewis acids (such as B(3+), Al(3+) and Sn(4+)) and can be applied to other 2D materials (for example MoS2, MoSe2). Finally, we show that it is possible to use Lewis acid-base chemistry as a bridge to connect molecules to 2D atomic layers and fabricate a proof-of-principle dye-sensitized photosensing device.