Murphy equalised in the 85th minute for Stanley after giving the home side the lead early in the second half.
Pompey's strikeforce of Patrick Agyemang and David Connolly looked lively from the start. Agyemang had a low shot which was superbly saved by Ian Dunbavin in the Stanley goal on 40 minutes.
Accrington went ahead early in the second half when defender Murphy collected a pass from Danny Webber on the inside right and hit a curling cross into the far corner.
But Pompey equalised when Agyemang headed down for Connolly to fire in from eight yards out in the 57th minute.
Dunbavin then saved efforts from Romain Padovani and Andy Barcham as Pompey looked for the winner.
Portsmouth were given a penalty on 78 minutes when Agyemang was brought down with a shoulder charge before Connolly was also felled in the box.
And Connolly stepped up and fired into the bottom corner to give Pompey the lead.
But Stanley equalised five minutes from time when Murphy headed in from close range following a header across goal from Tom Aldred.
Portsmouth's Barcham then hit the post with a low, curling shot from inside the box and Dunbavin saved Jed Wallace's follow-up shot.