The Billikens (0-6), who were trailing 4-0, did not give up and got a score from Lycett at 40:03, finishing a Lexie Lindblad pass for Lycett's team-high-tying third goal of the season.
A little more than five minutes later, SLU pulled it to 4-2 on Murphy's first career goal. Laken Gehris earned an assist on the play.
Missouri State goalie Andrea Bain held SLU scoreless the rest of the way, including stopping a Gehris penalty shot in the final minute of action.
MSU (1-3) scored three times in the first half, and once again early in the second session. Olivia Nicotera scored twice for the Bears, while Sydney Richelieu notched a goal and an assist.
Saint Louis returns to action Sunday, Sept. 9, when it hosts Georgetown at Soccer Park. First whistle is scheduled for 1 p.m.