Murphy scored from close range after the home defence failed to clear Piero Mingoia's left-wing cross to take a vital three points for the division's bottom club.
Accrington took the lead in the 19th minute through a controversial penalty. Barry Roche was harshly adjudged to have brought down James Gray and Danny Webber stepped up to send the Morecambe goalkeeper the wrong way from the spot.
The home side hit back in the 49th minute when Jack Sampson scored his third of the season from close range after the ball ran free to him in the box following an excellent save from keeper Marcus Bettinelli.
Morecambe defender Tony Diagne wasted two glorious before Murphy popped up to take the points.
The win means Stanley have never lost to Morecambe in 13 Football League games.