The self-polarization of PbZr0.52Ti0.48O3 thin film is switched by changing film thickness through the competition between the strain relaxation-induced flexoelectric fields and the interfacial effects. Without an applied electric field, this reversal of self-polarization is exploited to control the magnetic properties of La0.67Sr0.33MnO3 by the competition/cooperation between the charge-mediated and the strain-mediated effects. Scanning transmission electron microscopy, polarized near edge x-ray absorption spectroscopy, and half-integer diffraction measurements are employed to decode this intrinsic magnetoelectric effects in La0.67Sr0.33MnO3/PbZr0.52Ti0.48O3 heterostructures. With PbZr0.52Ti0.48O3 films < 48 nm, the self-polarization-driven carrier density modulation around La0.67Sr0.33MnO3/PbZr0.52Ti0.48O3 interface and the strain-mediated Mn 3d orbital occupancy work together to enhance magnetism of 14 unit cells La0.67Sr0.33MnO3 film; with PbZr0.52Ti0.48O3 layers > 48 nm, the strain-induced the change of bond length/angle of MnO6 accompanied with a modified spin configuration are responsible for the decrease in Curie temperature and magnetization of 14 unit cells La0.67Sr0.33MnO3 film.