In this paper, we establish and calibrate mid-infrared (MIR) hydrogen recombination lines observed with the James Webb Space Telescope as accretion tracers for pre-main-sequence stars that accrete from circumstellar disks. This work is part of a coordinated, multi-observatory effort that monitored the well-known binary system DQ Tau over three orbital periods, capturing its periodic accretion bursts. In this first paper, we present nine epochs of Mid-Infrared Instrument (MIRI) Medium Resolution Spectrometer (MRS) spectra with near-simultaneous Las Cumbres Observatories (LCO) photometry and Very Large Telescope X-shooter spectroscopy. This program caught exceptional accretion variability, spanning almost 2 orders of magnitude between the peak of the first periastron accretion burst and the following quiescent phases. The MIRI spectra show H I line luminosities that vary in step with the accretion-luminosity time series measured with LCO and X-shooter. The tight correlation with accretion and the large line widths, which MIRI resolves for the first time, support an accretion-flow origin for MIR H I transitions. Combining these three exceptional data sets, we derive accurate relations between MIR line and accretion luminosities for three H I transitions (10–7, 7–6, and 8–7), and improve upon a previous relation based on Spitzer spectra. These new relations equip the community with a direct measurement of the accretion luminosity from MIRI-MRS spectra. A MIRI-derived accretion luminosity is fundamental for time-domain chemistry studies, as well as for studies of accretion in embedded/distant sources that are currently inaccessible in the optical. With these new relations, we provide accretion luminosities for an archival sample of 38 MRS spectra of protoplanetary disks published to date.