Wade gained revenge for two European Tour semi-final defeats at the hands of world number two Wright earlier this year with a 6-4 success in a high-quality game in which both men averaged over 101.
The left-hander will take on Jonny Clayton on in Sunday afternoon's last 16 after the Welshman defeated last weekend's German Darts Open champion Max Hopp 6-3.
Suljovic produced the performance of the day as he averaged 106.29 in a 6-1 demolition of Darius Labanauskas, with the aid of crowd-pleasing checkouts of 121 and 102.
The Austrian ace fired in five 180s as he set up a third round tie with Spain's Cristo Reyes, who claimed a comfortable 6-2 victory against Jelle Klaasen.
World Champion Rob Cross survived a huge scare against Steve West, who led 5-3 and missed seven darts to beat the number two seed.
Cross, the pre-tournament favourite to win the £25,000 title, will take on Steve Beaton after the veteran star edged out Luke Humphries in a match that went all the way to a last-leg decider.
Third seed Michael Smith bounced back from last weekend's German Darts Open final defeat to Hopp with a whitewash win over Michael Barnard, in which the Unibet Premier League star didn't miss a dart at a double and averaged 104.86.
The 27-year-old's pursuit of a fifth PDC European Tour title will continue with a Sunday afternoon clash against Dimitri Van den Bergh.
Reigning PDC Unicorn World Youth Champion Van den Bergh defeated Benito van de Pas 6-4 to progress to the final day of action.
World Grand Prix champion Daryl Gurney won six out of seven legs to defeat Ron Meulenkamp after trailing the Dutchman 2-0.
Gurney will face Darren Webster in the third round after the 49-year-old edged out Richie Burnett in a last-leg shoot-out.
Webster stormed into a 4-1 lead but the Welshman roared back, winning four legs on the spin before missing the bull for a match-winning 121 finish, allowing the Norwich man to level and then break to seal victory.
Mervyn King romped to victory in the opening match of round two, defeating Ireland's Jason Cullen 6-0.
King will face another Cullen in the last 16 after Joe also produced a dominant performance against an Irishman.
The Yorkshire ace landed a 108 finish in the first leg of his 6-2 success over Steve Lennon, which he sealed by taking out 107.
Gerwyn Price also enjoyed a comfortable win, defeating Bolton's Scott Taylor 6-2 to set up a last 16 meeting with Wayne Jones, who received a bye following the withdrawal of Dave Chisnall.
Ian White defeated Brendan Dolan 6-4 as he followed a sublime 129 checkout in the penultimate leg with a maximum that helped him break to clinch victory.
White will take on Simon Whitlock on Sunday after the Australian won an edgy affair against Adam Hunt 6-4.
The £135,000 tournament concludes on Sunday across two sessions, with the last 16 stage being played in the afternoon before the quarter-finals, semi-final and final take place in the evening.
The Austrian Darts Open will be broadcast throughout the weekend for PDCTV-HD Subscribers, and through a series of bookmakers' websites worldwide listed below.
Saturday Results
Afternoon Session
- Mervyn King 6-0 Jason Cullen
- Gerwyn Price 6-2 Scott Taylor
- Steve Beaton 6-5 Luke Humphries
- Ian White 6-4 Brendan Dolan
- Joe Cullen 6-2 Steve Lennon
- Michael Smith 6-0 Michael Barnard
- Dimitri Van den Bergh 6-4 Benito van de Pas
- Wayne Jones Bye (Due to Dave Chisnall's withdrawal)
Evening Session
- Darren Webster 6-5 Richie Burnett
- Daryl Gurney 6-3 Ron Meulenkamp
- Simon Whitlock 6-4 Adam Hunt
- Cristo Reyes 6-2 Jelle Klaasen
- Rob Cross 6-5 Steve West
- Jonny Clayton 6-3 Max Hopp
- James Wade 6-4 Peter Wright
- Mensur Suljovic 6-1 Darius Labanauskas
Sunday Schedule
Afternoon Session (1pm local time, 12pm BST)
Third Round
- Michael Smith v Dimitri Van den Bergh
- Joe Cullen v Mervyn King
- Wayne Jones v Gerwyn Price
- Rob Cross v Steve Beaton
- Daryl Gurney v Darren Webster
- Mensur Suljovic v Cristo Reyes
- Ian White v Simon Whitlock
- James Wade v Jonny Clayton
Evening Session (7.15pm local time, 6.15pm BST)]
Quarter-Finals
Semi-Finals
Final
Sunday's games played in draw bracket order.
Format
Third Round & Quarter-Finals - best of 11 legs
Semi-Finals - best of 13 legs
Final - best of 15 legsRelated links
Fast Results
Scores
Racecards 
