Abstruse learning algorithms and complex datasets increasingly characterize modern clinical decision support systems (CDSS). As a result, clinicians cannot easily or rapidly scrutinize the CDSS recommendation when facing a difficult diagnosis or treatment decision in practice. Over-trust or under-trust are frequent. Prior research has explored supporting such assessments by explaining DST data inputs and algorithmic mechanisms. This paper explores a different approach: Providing precisely relevant, scientific evidence from biomedical literature. We present a proof-of-concept system, Clinical Evidence Engine, to demonstrate the technical and design feasibility of this approach across three domains (cardiovascular diseases, autism, cancer). Leveraging Clinical BioBERT, the system can effectively identify clinical trial reports based on lengthy clinical questions (e.g., "risks of catheter infection among adult patients in intensive care unit who require arterial catheters, if treated with povidone iodine-alcohol"). This capability enables the system to identify clinical trials relevant to diagnostic/treatment hypotheses -- a clinician's or a CDSS's. Further, Clinical Evidence Engine can identify key parts of a clinical trial abstract, including patient population (e.g., adult patients in intensive care unit who require arterial catheters), intervention (povidone iodine-alcohol), and outcome (risks of catheter infection). This capability opens up the possibility of enabling clinicians to 1) rapidly determine the match between a clinical trial and a clinical question, and 2) understand the result and contexts of the trial without extensive reading. We demonstrate this potential by illustrating two example use scenarios of the system. We discuss the idea of designing DST explanations not as specific to a DST or an algorithm, but as a domain-agnostic decision support infrastructure.