Trump's second hundred of the match had pulled the score back to 4-3, but Murphy accumulated a break of 52 to give him the advantage and maintained this with superior safety play to book a place in the semi-finals.
Murphy won the first frame thanks to a fluke on the last pink when 12 points in front but Trump replied with a 126 in the following frame.
'Oh wow! A mighty big fluke!' - Murphy gets huge slice of luck against Trump
A 96-break put Murphy back in front and then he came back from a 70 deficit in the fourth frame to claim a 3-1 lead at the break.
After Trump won the first of the second session, an hundred break (101) restored the two frame advantage, before the reigning world champion reached three figures to force a nervous finish.
'Immaculate' - Trump responds with masterful 126 break
Murphy also dispatched Trump in the Masters in January and feels he is a match for one of the most talented players of the modern era.
"Yeah I think in a match like at the Masters where he had three centuries and I still won 6-3, I think that sort of gives you an air of, ‘I can take his best punches and I can get off the canvas and hit him back'," Murphy said on Eurosport.
"But great things were and have been expected of Judd all his career, they are now coming true so when you go up against him, you know that you have to bring your A-game, or otherwise you might not bother."
Murphy will now play Yan Bingtao who beat John Higgins 5-2, a cool 61 break to the final pink putting him through at the expense of the Scot.
"He’s just coming, isn’t he? He’s coming for us all," Murphy said of his next opponent. "I was having a little glance over at some stage. He was just going for his shots and potting most of them and that’s how he plays and any time you beat someone like John Higgins, it’s a massive, massive achievement so he will be buzzing tomorrow."
Ronnie O'Sullivan, fresh from his sensational win over Mark Selby, faces Kyren Wilson in the other semi-final.
Ronnie O'Sullivan v Kyren Wilson
Shaun Murphy v Yan Bingtao