Coulomb attraction between electrons and holes in a narrow-gap semiconductor or a semimetal is predicted to lead to an elusive phase of matter dubbed excitonic insulator. However, direct observation of such electronic instability remains extremely rare. Here, we report the observation of incipient divergence in the static excitonic susceptibility of the candidate material Ta2NiSe5 using Raman spectroscopy. Critical fluctuations of the excitonic order parameter give rise to quasi-elastic scattering of B-2g symmetry, whose intensity grows inversely with temperature toward the Weiss temperature of T-W approximate to 237 K, which is arrested by a structural phase transition driven by an acoustic phonon of the same symmetry at T-C=325 K. Concurrently, a B-2g optical phonon becomes heavily damped to the extent that its trace is almost invisible around T-C, which manifests a strong electron-phonon coupling that has obscured the identification of the low-temperature phase as an excitonic insulator for more than a decade. Our results unambiguously reveal the electronic origin of the phase transition. Concominant structural and electronic phase transitions in the excitonic insulator candidate Ta2NiSe5 make the identification of the driving mechanism of the transition challenging. Here, the authors report evidence for electronically-driven transition via Raman susceptibility measurements.