The seven-times world champion made breaks of 71 and 77 on his way to securing a meeting with Aaron Canavan in the last eight on Friday at 1pm at Sheffield's Crucible Theatre.
The Scotsman also made a cool clearance of 45 to keep alive his hopes by closing to 3-2 behind.
Michael Judge closed with a 60 break in a 4-1 win over 1985 world champion Dennis Taylor.
Defending champion Jimmy White will face Tony Knowles or Peter Lines in the last eight on Friday night.
First round results
- Ken Doherty (Ire) 4-3 Rodney Goggins (Ire)
- Patrick Wallace (NI) 2-4 Darren Morgan (Wal)
- Jimmy White (Eng) 4-1 Joe Johnson (Eng)
- Aaron Canavan (Jer) 4-3 Leo Fernandez (Ire)
- Stephen Hendry (Sco) 4-3 Nigel Bond (Eng)
- Wayne Cooper (Eng) 4-2 Gary Filtness (Eng)
- Michael Judge (Ire) 4-1 Dennis Taylor (NI)
- Tony Knowles (Eng) 0-4 Peter Lines (Eng)
- Stephen Hendry (Sco) 4-1 Aaron Canavan (Jer)
- Wayne Cooper v Michael Judge
- Ken Doherty v Darren Morgan
- Jimmy White v Peter Lines