Hot electron preheat is a major obstacle on the way to achieving higher gain in inertial confinement fusion. Broadband laser drivers are pursued to suppress laser plasma instabilities and resulting hot electrons, yet recent moderate-bandwidth experiments have instead found enhanced hot electron production of unclear origin. Our direct-drive-relevant experiments on the low-coherence Kunwu laser facility identify two-plasmon decay (TPD) as the primary source of hot electrons, and demonstrate for the first time that moderate-bandwidth laser pulses can enhance TPD when the interaction remains above the TPD threshold. Using particle-in-cell simulations, we attribute this TPD enhancement and the consequent hot electron production to stochastic intensity spikes inherent in broadband laser fields, across both weakly and strongly driven regimes. These findings provide new physical insights into reducing hot electron preheat with broadband laser drivers.