Musto entered the final round five strokes back and in 12th place.
The Mids will play 36 holes on Monday and 18 on Tuesday.
Hurrican Nate threatened to wash out the David Toms Intercollegiate, shortening it by a full day and a round.
This will be the Mids' third straight appearance at the David Toms Intercollegiate in Baton Rouge.
The match went down to the wire as Army and Navy split the first six singles matches on Sunday.