The rotational spectrum of 3-furonitrile has been collected from 85 to 500 GHz, spanning the most intense rotational transitions observable at room temperature. The large dipole moment imparted by the nitrile substituent confers substantial intensity to the rotational spectrum, enabling the observation of over 5600 new rotational transitions. Combined with previously published transitions, the available data set was least-squares fit to partial-octic, distorted-rotor A- and S-reduced Hamiltonian models with low statistical uncertainty (σfit < 0.031 MHz) for the ground vibrational state. Similar to its isomer 2-furonitrile, the two lowest-energy vibrationally excited states of 3-furonitrile (ν17, ν24), which correspond to the in-plane and out-of-plane nitrile bending vibrations, form an a- and b-axis Coriolis-coupled dyad. Rotationally resolved infrared transitions (30-600 cm-1) and over 4200 pure rotational transitions for both ν17 and ν24 were fit to a partial-octic, Coriolis-coupled, two-state Hamiltonian with low statistical uncertainty (σfit rot < 0.045 MHz, σfit IR < 6.1 MHz). The least-squares fitting of these vibrationally excited states provides their accurate and precise vibrational frequencies (ν17 = 168.193 164 8 (67) cm-1 and ν24 = 169.635 831 5 (77) cm-1) and seven Coriolis-coupling terms (Ga, GaJ, GaK, Fbc, FbcK, Gb, and Fac). The two fundamental states exhibit a notably small energy gap (1.442 667 (10) cm-1) and an inversion of the relative energies of ν17 and ν24 compared to those of the isomer 2-furonitrile. The rotational frequencies and spectroscopic constants of 3-furonitrile that we present herein provide a sufficient basis for conducting radioastronomical searches for this molecule across the majority of the frequency range available to current radiotelescopes.