Leam Richardson's men moved five points clear of the drop zone ahead of Saturday's games as they continued their strong form against the Shrimps, who are now without a win over Stanley in 12 league attempts.
Murphy, who scored a last-gasp equaliser at York on Saturday, opened the scoring after 28 minutes against the run of play.
Lee Molyneux's low 30-yard free kick was deflected into the net by the defender to wrong-foot goalkeeper Barry Roche.
Morecambe looked dangerous at times with Robbie Threlfall's in-swinging corner tipped over by home keeper Paul Rachubka.
But Stanley's defence held firm and the home side scored their second from a counter attack as the hour approached.
Rommy Boco ran from midfield and rounded Roche but his shot was blocked. The ball fell to Amond, who blasted home from 12 yards through Chris Doyle's legs to seal a crucial win.