IM Per is a triple star system whose eclipsing pair masses and radii are accurate to within 1%. The Transiting Exoplanet Survey Satellite (TESS) light curve of the program target exhibits partial eclipses and multiple oscillations with millimagnitude-level amplitudes. It is found that the oscillations affect eclipse timing measurements. Binary modeling of the high-quality TESS data indicates that the eclipsing components of the triple system are twin dwarfs with parameters of M2/M1=0.995, R2/R1=0.901, and Δ(Teff,1-Teff,2)=12 K in an eccentric (e = 0.049), detached configuration. The third light of l3=0.054 may mostly come from a G-type tertiary companion. Our predicted parallax of 1.52±0.09 mas is concurrent with the Gaia measurement of 1.52±0.05 mas. Multifrequency analysis of the outside-eclipse residuals reveals 22 significant pulsation signals: 4 in the gravity-mode region (0.03？2.22 day？1) and 18 in the pressure-mode region (9.19？25.12 day？1). Of the low frequencies, f11 and f14 are orbital harmonics that can be identified as tidally excited modes. The pulsation periods and constants for the high frequencies, and the position in the Cepheid instability strip demonstrate that the pulsating component of IM Per is a δ Sct variable.