The paper describes SeamlessVR, a method for switching effectively from immersive visualization, in a virtual reality (VR) headset, to non-immersive visualization, on screen. SeamlessVR implements a continuous morph of the 3D visualization to a 2D visualization that matches what the user will see on screen after removing the headset. This visualization continuity reduces the cognitive effort of connecting the immersive to the non-immersive visualization, helping the user continue on screen a visualization task started in the headset. We have compared SeamlessVR to the conventional approach of directly removing the headset in an IRB-approved user study with N = 30 participants. SeamlessVR had a significant advantage over the conventional approach in terms of time and accuracy for target tracking in complex abstract and realistic scenes and in terms of participants' perception of the switch from immersive to non-immersive visualization, as well as in terms of usability. SeamlessVR did not pose cybersickness concerns.