We independently determine the zero-point offset of the Gaia early Data Release-3 (EDR3) parallaxes based on ~110,000 W Ursae Majoris (EW)-type eclipsing binary systems. EWs cover almost the entire sky and are characterized by a relatively complete coverage in magnitude and color. They are an excellent proxy for Galactic main-sequence stars. We derive a W1-band period–luminosity relation with a distance accuracy of 7.4%, which we use to anchor the Gaia parallax zero-point. The final, global parallax offsets are −28.6 ± 0.6 μas and −25.4 ± 4.0 μas (before correction) and 4.2 ± 0.5 μas and 4.6 ± 3.7 μas (after correction) for the five- and six-parameter solutions, respectively. The total systematic uncertainty is 1.8 μas. The spatial distribution of the parallax offsets shows that the bias in the corrected Gaia EDR3 parallaxes is less than 10 μas across 40% of the sky. Only 15% of the sky is characterized by a parallax offset greater than 30 μas. Thus, we have provided independent evidence that the parallax zero-point correction provided by the Gaia team significantly reduces the prevailing bias. Combined with literature data, we find that the overall Gaia EDR3 parallax offsets for Galactic stars are [−20, −30] μas and 4–10 μas, respectively, before and after correction. For specific regions, an additional deviation of about 10 μas is found.