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During a search for X-ray transients in the XMM–Newton archive within the EXTraS project, we discovered a new X-ray source that is detected only during an ∼5 min interval of an ∼21 hr-long observation performed on 2011 June 21 (EXMM 023135.0–603743, probability of a random Poissonian fluctuation: ∼1.4 × 10−27). With dedicated follow-up observations, we found that its position is consistent with a star-forming galaxy (SFR = 1–2 M⊙ yr−1) at redshift z = 0.092 ± 0.003 (d = 435 ± 15 Mpc). At this redshift, the energy released during the transient event was 2.8 × 1046 erg in the 0.3–10 keV energy band (in the source rest frame). The luminosity of the transient, together with its spectral and timing properties, make EXMM 023135.0–603743 a gripping analog to the X-ray transient associated to SN 2008D, which was discovered during a Swift/XRT observation of the nearby (d = 27 Mpc) supernova-rich galaxy NGC 2770. We interpret the XMM–Newton event as a supernova shock break-out or an early cocoon, and show that our serendipitous discovery is broadly compatible with the rate of core-collapse supernovae derived from optical observations and much higher than that of tidal disruption events. [ABSTRACT FROM AUTHOR]