In this Letter, we report detections of SiO v=3 J=1--0 maser emission in very long baseline interferometric (VLBI) observations towards 4 out of 12 long-period variable stars: WX Psc, R Leo, W Hya, and T Cep. The detections towards WX Psc and T Cep are new ones. We also present successful astrometric observations of SiO v=2 and v=3 J=1--0 maser emissions associated with two stars: WX Psc and W Hya and their position-reference continuum sources: J010746.0+131205 and J135146.8-291218 with the VLBI Exploration of Radio Astrometry (VERA). The relative coordinates of the position-reference continuum source and SiO v=3 maser spots were measured with respect to those of an SiO v=2 maser spot adopted as fringe-phase reference. Thus the faint continuum sources were inversely phase-referenced to the bright maser sources. It implies possible registration of multiple SiO maser line maps onto a common coordinate system with 10 microarcsecond-level accuracy.