We report on serendipitous Euclid observations of previously known transients, using the Euclid Q1 data release. By cross-matching with the Transient Name Server (TNS) we identify 164 transients that coincide with the data release. Although the Euclid Q1 release only includes single-epoch data, we are able to make Euclid photometric measurements at the location of 161 of these transients, where 67 had a significant flux measurement in at least one band. Euclid obtained deep photometric measurements or upper limits of these transients in the IE, YE, JE, and HE bands at various phases of the transient light curves, including before, during, and after the observations of ground-based transient surveys. Approximately 70% of known transients reported in the six months before the Euclid observation date and with a discovery magnitude brighter than 24 were detected in Euclid IE images. Our observations include one of the earliest near-infrared detections of a Type Ia supernova (SN 2024pvw) 15 days prior to its peak brightness, and the late-phase (435.9 days post peak) observations of the enigmatic core-collapse SN 2023aew. Euclid deep photometry provides valuable information on the nature of these transients such as their progenitor systems and power sources, with late-time observations being a uniquely powerful contribution. In addition, Euclid is able to detect the host galaxies of some transients that were previously classed as hostless. The Q1 data demonstrate the power of the Euclid data even with only single-epoch observations available, as will be the case for much larger areas of sky in the Euclid Wide Survey.