We present the discovery of a peculiar X-ray transient, EP241021a, by the Einstein Probe (EP) mission and the results from multiwavelength follow-up observations. The transient was first detected with the Wide-field X-ray Telescope as an intense flare lasting for ∼100 s, reaching a luminosity of L0.5‑4 keV ≈ 1048 erg s‑1. Further observations with EP's Follow-up X-ray Telescope reveal a huge drop in the X-ray flux by a factor of >1000 within 1.5 days. After maintaining a nearly plateau phase for ∼7 days, the X-ray flux decreases ∝t‑1.2 over a period of ∼30 days, followed by a sudden decrease to an undetectable level by EP and XMM-Newton, making it the longest afterglow emission detected among known fast X-ray transients. Bright counterparts at optical and radio wavelengths were also detected, with high peak luminosities in excess of 1044 erg s‑1 and 1041 erg s‑1, respectively. In addition, EP241021a exhibits a nonthermal X-ray spectrum, red optical color, X-ray and optical rebrightenings in the light curves, and fast radio spectral evolution, suggesting that relativistic jets may have been launched. We discuss the possible origins of EP241021a, including a choked jet with supernova shock breakout, a merger-triggered magnetar, a highly structured jet, and a repeating partial tidal disruption event involving an intermediate-mass black hole, but none can perfectly explain the multiwavelength properties. EP241021a may represent a new type of X-ray transient with month-duration evolution timescales; future EP detections and follow-up observations of similar systems will provide statistical samples to understand the underlying mechanisms at work.