Nathan Aspinall produced one of the greatest fightbacks in European Tour history on Saturday to go along with Suljovic's stunning upset.
Gibraltar's Victoria Stadium is playing host to the year's final PDC European Tour event, with £140,000 and places in the forthcoming Cazoo European Championship on offer.
Price will be among the leading names to feature in Dortmund, but the Welshman was sent packing in Gibraltar by a nerveless Suljovic, as the Austrian exacted revenge for his 8-0 defeat to Price in last year's final.
Price converted 110 and 160 checkouts to establish a 3-2 lead, but Suljovic responded superbly, winning four of the last five legs courtesy of back-to-back 13-darters in the closing stages.
However, Aspinall stole the headlines with an astonishing fightback against Vincent van der Voort, recovering from 5-0 down to stun the Dutchman earlier in the afternoon.
Van der Voort punished an abject start from Aspinall to establish a commanding cushion, but after squandering five match darts for a 6-1 success, the Dutchman began to falter and Aspinall came roaring back.
The World Grand Prix runner-up followed up a 121 finish in leg eight with 14 and 15-darters to restore parity at five apiece, before surviving two more match darts in an extraordinary finale, pinning double four to complete the comeback.
Michael van Gerwen - who defeated Aspinall to claim World Grand Prix glory last weekend - underlined his title credentials with a sparkling display against Steve Beaton, averaging over 106 to triumph 6-3 in a high-quality tussle.
The three-time champion fired in three 180s and took out a wonderful 130 finish on the bull to continue his blistering form, as Beaton bowed out despite averaging 102.
World Champion Peter Wright ended home hopes in Gibraltar, reeling off five consecutive legs to close out an emphatic 6-2 win against Host Nation Qualifier Craig Galliano.
Galliano - granted a day off from his work as a police officer, raised the roof with a superb 120 checkout in leg two, but consecutive 14-darters and a 116 combination from Wright midway through the match curtailed the 20-year-old's hopes of a shock victory.
Top seed Luke Humphries produced a sumptuous display of scoring in his tie against Kenny Neyens, averaging 99, landing five 180s and registering a brace of 11-darters to record a 6-3 win over the Belgian qualifier.
Second Round Results, Saturday October 15, Afternoon Session:
- Rob Cross 6-3 Rusty-Jake Rodriguez
- Ryan Searle 6-3 William O'Connor
- Wesley Plaisier 6-3 Dave Chisnall
- Dirk van Duijvenbode 6-5 Jason Lowe
- Ryan Joyce 6-5 Danny Noppert
- Jose de Sousa 6-3 Rowby-John Rodriguez
- Damon Heta 6-4 Chris Dobey
- Nathan Aspinall 6-5 Vincent van der Voort
Humphries - competing for the first time since the birth of his first child, Rowan, earlier this week - will now take on Wesley Plaisier, who preserved his European Championship qualification hopes with a 6-3 victory over Belgian Darts Open champion Dave Chisnall.
Plaisier defied a ton-plus average from Chisnall to prevail in a high-quality tussle, taking out a 126 combination in leg six before capping off a clinical display with a fine 101 checkout.
Emerging star Josh Rock continued his dream 2022 campaign with a 6-3 win over former Gibraltar Darts Trophy winner Michael Smith, converting six of his 11 attempts at double to set up a mouth-watering last 16 tie against Jonny Clayton.
Clayton swept aside Stephen Bunting 6-2 in convincing fashion to reach Sunday's third round - kicking off proceedings with a 122 checkout - with Bunting unable to replicate the 105 average he produced in his first round win over Daryl Gurney.
World Cup winner Damon Heta moved through to Sunday's final stages with a battling 6-4 win over Chris Dobey, and he will now renew his rivalry with Masters champion Joe Cullen, who survived a late onslaught from Ritchie Edhouse to prevail by the same scoreline.
Dirk van Duijvenbode survived a scare against Jason Lowe to book a meeting with comeback king Aspinall in round three, while Jose De Sousa will face Van Gerwen on Sunday afternoon, after claiming a 6-3 win over a returning Rowby-John Rodriguez.
Second Round Results, Saturday October 15, Evening Session:
- Josh Rock 6-3 Michael Smith
- Luke Humphries 6-3 Kenny Neyens
- Peter Wright 6-2 Craig Galliano
- Jonny Clayton 6-2 Stephen Bunting
- Michael van Gerwen 6-3 Steve Beaton
- Mensur Suljovic 6-4 Gerwyn Price
- Gabriel Clemens 6-1 Dimitri Van den Bergh
- Joe Cullen 6-4 Ritchie Edhouse
Elsewhere, fifth seed Rob Cross defied a late rally from Austrian youngster Rusty-Jake Rodriguez in Saturday's opener, and his reward is match-up against Ryan Joyce, who battled back from 5-3 adrift to dump out UK Open champion Danny Noppert.
Searle will take on World Champion Wright in the last 16, averaging 98 and conjuring up two ton-plus finishes to end William O'Connor's European Championship qualification hopes.
Meanwhile, Gabriel Clemens will face Price's conqueror Suljovic for a place in the last eight, after winning six straight legs to demolish a below-par Dimitri Van den Bergh 6-1 in the penultimate match of the evening.
Third Round Matches, Sunday October 16, Afternoon Session:
- Luke Humphries v Wesley Plaisier
- Ryan Searle v Peter Wright
- Josh Rock v Jonny Clayton
- Rob Cross v Ryan Joyce
- Michael van Gerwen v Jose De Sousa
- Nathan Aspinall v Dirk van Duijvenbode
- Mensur Suljovic v Gabriel Clemens
- Damon Heta v Joe Cullen
The last 16 will take place on Sunday afternoon, before the tournament concludes with the quarter-finals, semi-finals and final in a bumper evening session.
Plaisier will qualify for the European Championship with victory over Humphries, while Suljovic and Joyce must lift the title to seal their spots in Dortmund, with Dobey and Krzysztof Ratajski the two players in danger of missing out.
The tournament is being broadcast live on PDCTV, exclusively on DAZN in Germany, Austria and Switzerland, and through bookmakers' websites worldwide.
Third Round Matches, Sunday October 16, Evening Session: