Induced spin polarization of π-conjugated carbon and h-BN low dimensional fragments at the interfaces formed by deposition of pentacene molecule and narrow zigzag graphene and h-BN nanoribbons on MnO2-terminated LSMO(001) thin film was studied using GGA PBE+U PAW D3-corrected approach. Induced spin polarization of π-conjugated low-dimensional fragments is caused by direct exchange with Mn ions of LSMO(001) MnO-derived surface. Due to direct exchange, the pentacene molecule changes its diamagnetic narrow-band gap semiconducting nature to the ferromagnetic semiconducting state with 0.15eV energy shift between spin-up and spin-down valence bands and total magnetic moment of 0.11μB. Direct exchange converts graphene nanoribbon to 100% spin-polarized half-metal with large amplitude of spin-up electronic density at the Fermi level. The direct exchange narrows the h-BN nanoribbon band gap from 4.04 to 1.72eV in spin-up channel and converts the h-BN ribbon semiconducting diamagnetic nature to a semiconducting magnetic one. The electronic structure calculations demonstrate a possibility to control the spin properties of low-dimensional π-conjugated carbon and h-BN fragments by direct exchange with MnO-derived LSMO(001) surface for spin-related applications.