The two-plasmon-decay instability (TPD) in the large-incidence-angle regime is studied via fluid and particle-in-cell (PIC) simulations. It is found that the TPD threshold in this regime within a narrow incidence angle range close to 60∘ can be orders of magnitude lower than the normal-incidence threshold. A threshold formula is proposed for this regime and is verified by fluid and PIC simulations. PIC simulations show significant laser absorption and energetic electron generation once TPD is excited. The incident angle and the laser spot size have a significant influence on the TPD in the large-incidence-angle regime. The low threshold and significant hot electron generation in this regime pose potentially unexpected preheating risks to inertial confinement fusion.