Higher education students in the science, technology, engineering, and mathematics (STEM) fields are actively engaged with coursework, and their emotional maturity may be underdeveloped. The aim of this qualitative study was to investigate whether interactive art-making can provide a potential space for STEM undergraduates to experience play and freely explore themselves. We introduced the mutual squiggle and story-making method (MSSM), an art-based method wherein a practitioner collaborates with a participant to create art, followed by semi-structured interviews. Thematic analysis of the interview transcripts from seven STEM undergraduates revealed four themes: personal joy and fulfillment, interaction as a pivotal aspect of play, acknowledging appropriate compromises, and a non-play experience. Our findings suggest that the potential space created by MSSM can help STEM students navigate play through picture-making and storytelling experiences. Practitioners who conduct art-making with clients should be aware that they are being observed by participants and exhibit playful attitudes. This study sheds light on lowering the barrier to seeking help among STEM students. Further studies involving different academic disciplines as target groups are required. Policymakers should be aware of the importance of positive emotions aroused in play for STEM undergraduates to seek psychological support.