Context. Trans-Neptunian objects (TNOs) and Centaurs are remnants of our planetary system formation, and their physical properties have invaluable information for evolutionary theories. Stellar occultation is a ground-based method for studying these distant small bodies and has presented exciting results. These observations can provide precise profiles of the involved body, allowing an accurate determination of its size and shape. Aims. The goal is to show that even single-chord detections of TNOs allow us to measure their milliarcsecond astrometric positions in the reference frame of the Gaia second data release (DR2). Accurate ephemerides can then be generated, allowing predictions of stellar occultations with much higher reliability. Methods. We analyzed data from various stellar occultation detections to obtain astrometric positions of the involved bodies. The events published before the Gaia era were updated so that the Gaia DR2 stellar catalog is the reference, thus providing accurate positions. Events with detection from one or two different sites (single or double chord) were analyzed to determine the event duration. Previously determined sizes were used to calculate the position of the object center and its corresponding error with respectto the detected chord and the International Celestial Reference System propagated Gaia DR2 star position. Results. We derive 37 precise astrometric positions for 19 TNOs and four Centaurs. Twenty-one of these events are presented here for the first time. Although about 68% of our results are based on single-chord detection, most have intrinsic precision at the submilliarcsecond level. Lower limits on the diameter of bodies such as Sedna, 2002 KX₁₄, and Echeclus, and also shape constraints on 2002 VE₉₅, 2003 FF₁₂₈, and 2005 TV₁₈₉ are presented as valuable byproducts. Conclusions. Using the Gaia DR2 catalog, we show that even a single detection of a stellar occultation allows improving the object ephemeris significantly, which in turn enables predicting a future stellar occultation with high accuracy. Observational campaigns can be efficiently organized with this help, and may provide a full physical characterization of the involved object, or even the study of topographic features such as satellites or rings.