Using hybrid density functional theory calculations with van der Waals correction, we show that polar boron nitride (BN) nanoribbons can be favorably aligned via substantial hydrogen bonding at the interfaces, which induces significant interface polarizations and sharply reduces the band gap of insulating ribbons well below the silicon range. The interface polarization can strongly couple with carrier doping or applied electric fields, yielding not only enhanced stability but also widely tunable band gap for the aligned ribbons. Furthermore, similar layer-by-layer alignment also effectively reduces the band gap of a 2D hydrogenated BN sheet and even turns it into metal. This novel strategy for band gap control appears to be general in semiconducting composite nanostructures with polar nonbonding interfaces and thus offers unique opportunities for developing nanoscale electronic and optical devices.