The seven-times world champion – who won the final three frames of his 4-3 win over Nigel Bond in the first round on Thursday night – will meet defending champion Jimmy White at 12pm in the semi-finals on Saturday.
White was a 4-1 winner over world number 117 Peter Lines. 'The Whirlwind' lost the first frame, but breaks of 79, 62 and 65 saw him set up another meeting with his old foe at their favourite venue.
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Six-times World Championship finalist White and Hendry last met in a competitive match at the Crucible in the first round in 1998 when White completed a 10-4 win, but their meetings are best remembered for the Scotsman's four wins in finals between 1990 and 1994.
Jimmy White of England (seated) and Stephen Hendry of Scotland (playing) during the World Snooker Championship Final at the Crucible in Sheffield on 2nd May 1994. Hendry defeated White 18-17.
Image credit: Eurosport
The 1994 final saw Hendry complete an 18-17 win to deny White, who infamously missed a black off the spot in the final frame when among the balls and poised for victory.
This latest meeting comes 25 years after they clashed in the semi-finals in 1995 when Hendry won 16-12 and made the third 147 break in Crucible history.
Hendry enjoyed runs of 81, 75, 60 and 53 against the 2018 winner Canavan to stay in the hunt for the £25,000 top prize and a place in the Champion of Champions tournament later this year.
"There was lots of good stuff and a couple of horror shows in there, but unfortunately me being me that's the ones I remember," said Hendry.
"I think I'm just lacking a bit of match composure, I think that's what it is.
"You need to composed at the table, and I'd like to be more composed at the table," added the Scotsman, who retired from the main professional tour in 2012.
"But I'm working on some good stuff. My long game was great today so I'm happy to still be in.
It would be amazing to play Jimmy out here again.
1997 world champion Ken Doherty and Michael Judge meet in an all-Irish semi-final at 2pm on Saturday with the final played over the best of nine frames from 7pm on Saturday night.
Doherty enjoyed breaks of 67, 72 and 80 in a 4-2 win over Darren Morgan in the last eight with Judge a 4-1 winner against Wayne Cooper.
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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)
- Jimmy White (Eng) 4-1 Peter Lines (Eng)
- Wayne Cooper (Eng) 1-4 Michael Judge (Ire)
- Ken Doherty (Ire) 4-2 Darren Morgan (Wal)
- Stephen Hendry (Sco) v Jimmy White (Eng)
- Ken Doherty (Ire) v Michael Judge (Ire)