First-principles calculations reveal that in divalent europium perovskites EuMO3 (M = Ti, Zr, and Hf), antiferromagnetic superexchange interactions via nd states of the B-site M cations (n = 3, 4, and 5, respectively) are enhanced by rotations of the MO6 octahedra. The octahedral rotations involved in a structural change from cubic $ Pm{\bar 3}m $ to orthorhombic Pbnm structures not only reduce energy gaps between the Eu 4f and M nd bands but also point the M nd orbitals at the Eu sites, leading to a significant overlap between the M nd and Eu 4f orbitals. These results reveal that the octahedral rotations are indispensable for antiferromagnetic ordering observed for EuZrO3 and EuHfO3, and put these perovskites into a class of materials exhibiting a novel type of strong coupling between their magnetism and octahedral rotations.