Selby eased past Mark Williams 5-1 but Murphy had to come from 4-2 down to complete a battling win 5-4 win over surprise package Jack Lisowski.
Neil Robertson continued his fine form with a 5-2 win over Dumbarton’s Marcus Campbell. The Australian has dropped just three frames so far and booked an appointment with Stephen Maguire, who cruised to a 5-1 victory over Stuart Bingham.
Selby won a scrappy opening frame on the colours before Williams’ 54 won the second.
Selby won the third before a clearance of 64 put him two ahead. An edgy fifth again went to Selby before he secured the win with a 72.
“It was quite similar to yesterday (against Ricky Walden), I didn’t play fantastic,” said Selby. “Mark had a lot of chances but he missed too many balls.
“He kept giving me chances and I managed to take them in the end.
“As long as I keep winning then I have the chance to play better, and I’m only two matches away now from winning the title. I feel relaxed and I’m enjoying playing.”
Having beaten Judd Trump and Mark Davis on his way to the last eight, Lisowski looked set to continue that run against Murphy – who although consistent has yet to win a title this season.
Breaks of 40 and 48 brought him level, before final-frame breaks of 41 and 36 secured his progression.
“There’s a fine line between winning and losing and I had a bit of luck at the right time,” admitted 30-year-old Murphy.
“Jack is a player we’re going to see a lot more of in the next ten or 15 years – we have glimpsed the future this week.
“People better learn how to say his name properly because he’s going to be around for a long time. He’s very talented and confident and he plays an aggressive style of snooker.
“Any match against Mark Selby is difficult and I will have to play the best I’ve played all week. My break-building is good when I get chances, so if my safety play is strong then who knows.”