Precise spin manipulation of single molecules is crucial for future molecular spintronics. However, it has been a formidable challenge due to the complexities of the strong molecule–substrate coupling as well as the response of the molecule to external stimulus. Here we demonstrate by density functional theory calculations that precise spin manipulation can be achieved by extra CO and NO molecules coordination to transition metal phthalocyanine (TMPc) (TM = Co, Fe, Mn) molecules deposited on metal–supported graphene; the spins of TMPc molecules are switched from S to S – ¹/₂ (|S – 1|) after NO (CO) coordination. With the aid of a combination of molecular orbitals (MO) theory and recently developed principal interacting spin–orbital (PISO) analysis, the impacts of NO and CO coordinations on both adsorption configuration and spin polarization of TMPc are well elucidated. We reveal the different coordination geometries that CO always coordinates axially to the TM center with a linear geometry, while NO prefers a bent geometry, which can be attributed to the competition between the σ- and π-type interactions according to the PISO analysis. Particularly, the NO–MnPc complex adopts a bent geometry deviating from the prediction by the existing Enemark–Feltham formalism. In addition, MO analysis suggests that during the CO coordination, the simultaneous existence of σ-donation and π-back-donation promotes electrons flowing from the d_z² to partially occupied d_π (d_xz and d_xz) orbitals with subsequent reordering of the TM d-orbitals, resulting in the spin transition of S → |S – 1|. In comparison, given that NO is regarded as NO^– when it adopts a bent geometry coordinating to the TM center, the complete (CoPc) or partial (FePc and MnPc) quenching of the molecular spins caused by NO coordination is attributed to the electron transfer from TM to NO. These theoretical findings provide important insights into relevant experiments and offer an effective design strategy to realize underlying single-molecular spintronics devices integrated with two-dimensional materials.