Context. QSO B1420+326 is a blazar classified as a flat-spectrum radio quasar (FSRQ). At the beginning of the year 2020, it was found to be in an enhanced flux state and an extensive multiwavelength campaign allowed us to trace the evolution of the flare. Aims. We search for very high-energy (VHE) gamma-ray emission from QSO B1420+326 during this flaring state. We aim to characterize and model the broadband emission of the source over different phases of the flare. Methods. The source was observed with a number of instruments in radio, near-infrared, optical (including polarimetry and spectroscopy), ultraviolet, X-ray, and gamma-ray bands. We use dedicated optical spectroscopy results to estimate the accretion disk and the dust torus luminosity. We performed spectral energy distribution modeling in the framework of combined synchrotron-self-Compton and external Compton scenario in which the electron energy distribution is partially determined from acceleration and cooling processes. Results. During the enhanced state, the flux of both SED components of QSO B1420+326 drastically increased and the peaks were shifted to higher energies. Follow-up observations with the MAGIC telescopes led to the detection of VHE gamma-ray emission from this source, making it one of only a handful of FSRQs known in this energy range. Modeling allows us to constrain the evolution of the magnetic field and electron energy distribution in the emission region. The gamma-ray flare was accompanied by a rotation of the optical polarization vector during a low -polarization state. Also, a new superluminal radio knot contemporaneously appeared in the radio image of the jet. The optical spectroscopy shows a prominent FeII bump with flux evolving together with the continuum emission and a MgII line with varying equivalent width.