A popular approach for 3D source localization using multiple microphones is the steered-response power method, where the source position is directly estimated by maximizing a function of three continuous position variables. Instead of directly estimating the source position, in this paper we propose an indirect, distance-based method for 3D source localization. Based on properties of Euclidean distance matrices (EDMs), we reformulate the 3D source localization problem as the minimization of a cost function of a single variable, namely the distance between the source and the reference microphone. Using the known microphone geometry and estimated timedifferences of arrival (TDOAs) between the microphones, we show how the 3D source position can be computed based on this variable. In addition, instead of using a single TDOA estimate per microphone pair, we propose an extension that enables to select the most appropriate estimate from a set of candidate TDOA estimates, which is especially relevant in reverberant environments with strong early reflections. Experimental results for different source and microphone constellations show that the proposed EDM-based method consistently outperforms the steered-response power method, especially when the source is close to the microphones.