Mutual gaze detection, i.e., predicting whether or not two people are looking at each other, plays an important role in understanding human interactions. In this work, we focus on the task of image-based mutual gaze detection, and propose a simple and effective approach to boost the performance by using an auxiliary 3D gaze estimation task during the training phase. We achieve the performance boost without additional labeling cost by training the 3D gaze estimation branch using pseudo 3D gaze labels deduced from mutual gaze labels. By sharing the head image encoder between the 3D gaze estimation and the mutual gaze detection branches, we achieve better head features than learned by training the mutual gaze detection branch alone. Experimental results on three image datasets show that the proposed approach improves the detection performance significantly without additional annotations. This work also introduces a new image dataset that consists of 33.1K pairs of humans annotated with mutual gaze labels in 29.2K images.