Higgins (pictured below) secured his meeting with Trump - who he defeated 18-15 to claim the last of his four world titles in 2011 - courtesy of a 5-0 win over Michael White.
Trump was never at his best, but showed stickability in some sticky conditions to come from 2-0, 3-2 and 4-3 behind to usurp Stevens.
He made a key break of 49 in the final frame to seal his progress.
"It was very humid and sticky so conditions were difficult," said Trump. "We know it's going to be hard at this event and you just have to prepare yourself for that and not get down about it. Maybe Matthew got more distracted than I did."
2005 world champion Shaun Murphy will face Ding Junhui in arguably the most attractive encounter of the last 16.
Murphy enjoyed a 5-1 win over Mark King with Ding claiming the last three frames to deny Pankay Advani of India a famous success with a 5-4 victory.
Advani left himself on the cusp of the last eight with efforts of 86 and 76 earning him a 4-2 advantage after the pair split the first four frames, but Ding kept his composure to produce some of his very best stuff with 52, 136 and 86 enough to delight the locals.
Ding is bidding for a fifth ranking title this season having lost 9-3 to Ronnie O'Sullivan in the final of the recent Welsh Open.
Defending champion Mark Allen remains on course for a third straight Haikou World Open after a 5-3 win over former world champion Mark Williams.
He will meet Ricky Walden, who was never troubled in a 5-1 win over 1997 world champion Ken Doherty.
World number one Neil Robertson showed his class with a 5-1 drubbing of Rory McLeod. The Australian ran in 111 and 116 to take his tally of centuries to the season to 91 - just nine short of a record 100 tons for the season.
"It was a game of patience because Rory is a good safety player and doesn't make many mistakes," said Robertson, who faces Marco Fu for a place in the last eight.
"There were a few people moving around in the crowd including a woman with a baby. I missed one shot because someone was looking out from behind a pillar.
"I'm happy with the way I have played here so far but I think there's room for improvement. My best is good enough to win the tournament."
Haikou World Open
Wednesday's last 32 results
Mark Allen (NI) 5-3 Mark Williams (Wal)
Ken Doherty (Ire) 1-5 Ricky Walden (Eng)
John Higgins (Sco) 5-0 Michael White (Wal)
Matthew Stevens (Wal) 4-5 Judd Trump (Eng)
Thepchaiya Un-Nooh (Tha) 5-1 Andrew Higginson (Eng)
Ryan Day (Wal) 2-5 Graeme Dott (Sco)
Shaun Murphy (Eng) 5-1 Mark King (Eng)
Pankaj Advani (Ind) 4-5 Ding Junhui (Chn)
Mark Selby (Eng) 5-2 Noppon Saengkham (Thai)
Liang Wenbo (Chn) 5-3 Mark Davis (Eng)
Robert Milkins (Eng) 3-5 Alan McManus (Sco)
Dominic Dale (Wal) 5-4 Stuart Bingham (Eng)
Barry Hawkins (Eng) 4-5 Mark Joyce (Eng)
Ali Carter (Eng) 2-5 Kurt Maflin (Nor)
Marco Fu (HK) 5-3 Michael Holt (Eng)
Rory McLeod (Eng) 1-5 Neil Robertson (Aus)
Last 16 draw
Order of play: Thursday, March 13 (best of nine frames)
Mark Selby (Eng) v Liang Wenbo (Chn)
Alan McManus (Sco) v Dominic Dale (Wal)
Mark Joyce (Eng) v Kurt Maflin (Nor)
Marco Fu (HK) v Neil Robertson (Aus)
Mark Allen (NI) v Ricky Walden (Eng)
John Higgins (Sco) v Judd Trump (Eng)
Thepchaiya Un-Nooh (Tha) v Graeme Dott (Sco)
Shaun Murphy (Eng) v Ding Junhui (Chn)
- Sports & Recreation
- Shaun Murphy
- Ding Junhui
- Judd Trump
- Ricky Walden
- John Higgins
- Neil Robertson