The Einstein Probe (EP) achieved its first detection and localization of a bright X-ray flare, EP240219a, on 2024 February 19, during its commissioning phase. Subsequent targeted searches triggered by the EP240219a alert identified a faint, untriggered gamma-ray burst (GRB) in the archived data of Fermi Gamma-ray Burst Monitor (GBM), Swift Burst Alert Telescope (BAT), and Insight-HXMT/HE. The EP Wide-field X-ray Telescope (WXT) light curve reveals a long duration of approximately 160 s with a slow decay, whereas the Fermi/GBM light curve shows a total duration of approximately 70 s. The peak in the Fermi/GBM light curve occurs slightly later with respect to the peak seen in the EP/WXT light curve. Our spectral analysis shows that a single cutoff power-law (PL) model effectively describes the joint EP/WXT–Fermi/GBM spectra in general, indicating coherent broad emission typical of GRBs. The model yielded a photon index of ∼–1.70 ± 0.05 and a peak energy of ∼257 ± 134 keV. After detection of GRB 240219A, long-term observations identified several candidates in optical and radio wavelengths, none of which was confirmed as the afterglow counterpart during subsequent optical and near-infrared follow-ups. The analysis of GRB 240219A classifies it as an X-ray-rich GRB (XRR) with a high peak energy, presenting both challenges and opportunities for studying the physical origins of X-ray flashes, XRRs, and classical GRBs. Furthermore, linking the cutoff PL component to nonthermal synchrotron radiation suggests that the burst is driven by a Poynting flux-dominated outflow.