Murphy's layup with 2:50 remaining put the Bulldogs ahead for good, 49-48, in the defensive struggle between Missouri Valley Conference powers.
Loyola had two shots blocked in the final 15 seconds before Murphy made the clinching steal and was fouled.
Drake won despite shooting 33.3%. Loyola shot 35.1%. Cameron Krutwig and Aher Uguak scored 11 points apiece for the Ramblers.