We independently determine the zero-point offset of the Gaia early Data Release-3 (EDR3) parallaxes based on $sim 110,000$ 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 $-28.6pm0.6$ $mu$as and $-25.4pm4.0$ $mu$as (before correction) and $4.2pm0.5$ $mu$as and $4.6pm3.7$ $mu$as (after correction) for the five- and six-parameter solutions, respectively. The total systematic uncertainty is $1.8$ $mu$as. The spatial distribution of the parallax offsets shows that the bias in the corrected Gaia EDR3 parallaxes is less than 10 $mu$as across $40%$ of the sky. Only $15%$ of the sky is characterized by a parallax offset greater than 30 $mu$as. 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 $[-20, -30]$ $mu$as and 4-10 $mu$as, respectively, before and after correction. For specific regions, an additional deviation of about 10 $mu$as is found.
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