The four-time world champion had twice hauled himself level, from 2-1 and 3-2 down, before fending off the 24-year-old Welshman in a tight finish.
Selby will next meet Zhou Yuelong, who produced perhaps the day's biggest shock to knock out Luca Brecel.
From 4-2 down, Zhou reeled off three successive frames, including a marathon 52-minute decider, to stun the Belgian 5-4.
Elsewhere in the last eight, Jak Jones beat Aaron Hill while Mark Allen overcame Elliot Slessor to secure their semi-final berths.