Both were in scintillating form yesterday.
Flogas Irish Amateur Open champion Dawson recorded a thoroughly comprehensive 6&5 victory over Sweden’s Elis Svard in the last 16.
Kinsale star and St Andrews Links Trophy champion Murphy’s stunning recent run of form continued as made light work of the tournament’s top ranked player in world number five Viktor Hovland from Norway — also 6&5.
Dawson had earlier seen off Spaniard Victor Pastor by a two-hole margin while Murphy defeated American Walker Lee 4&2 in the round of 32.
“I played lovely golf,” said Dawson.
“I was really in control of my ball flight and just played really solid so I’m happy to come out on top.
“It’s a pity we have to play each other but it’s just another match really so we’ll see how we get on.”
Murphy, meanwhile, said: “I feel a lot more confident coming off the back of winning the St Andrews Links Trophy.
“I guess you could say I didn’t really have a name for myself before St Andrews but I got out there and managed to pick up the win.
“I feel I can win against the top ranked players in the world and I don’t think I would have felt that way without the victory at St Andrews.
“I’m feeling good and every part of my game is clicking.”
Joining the pair in the quarter-final is Portmarnock’s Conor Purcell who faces Australian David Micheluzzi.
Purcell got through with a 3&2 victory over Swede Adam Blomme having already recovered from three down to record a dramatic victory on the 19th over Walker Cup star and world number six Matthew Jordan.
He said: “This morning I was on the back foot going into the back nine and managed to get something out of it, and then the second game in the afternoon I played out of my skin.”
There was disappointment though for Rowan Lester and James Sugrue who both went out at the last 32 stage in Scotland.
Hermitage’s Lester went down by two holes against Englishman Ben Hutchinson, while Mallow’s Sugrue lost 3&2 against another Swede in Christoffer Palsson.
The other two quarter-finals this morning see South Africa’s Jovan Rebula taking on Englishman Tom Sloman, with Sloman’s compatriot Mitch Waite facing Palsson.