Extrasolar planets on eccentric short-period orbits provide a laboratory in which to study radiative and tidal interactions between a planet and its host star under extreme forcing conditions. Studying such systems probes how the planet's atmosphere redistributes the time-varying heat flux from its host and how the host star responds to transient tidal distortion. Here, we report the insights into the planet-star interactions in HAT-P-2's eccentric planetary system gained from the analysis of similar to 350 hr of 4.5 mu m observations with the Spitzer Space Telescope. The observations show no sign of orbit-to-orbit variability nor of orbital evolution of the eccentric planetary companion, HAT-P-2b. The extensive coverage allows us to better differentiate instrumental systematics from the transient heating of HAT-P-2b's 4.5 mu m photosphere and yields the detection of stellar pulsations with an amplitude of approximately 40 ppm. These pulsation modes correspond to exact harmonics of the planet's orbital frequency, indicative of a tidal origin. Transient tidal effects can excite pulsation modes in the envelope of a star, but, to date, such pulsations had only been detected in highly eccentric stellar binaries. Current stellar models are unable to reproduce HAT-P-2's pulsations, suggesting that our understanding of the interactions at play in this system is incomplete.