Bunting produced the first round's most outstanding display so far as he averaged 105.31 in a 6-3 victory over Gurney.
The pair traded early 11-darters, and Gurney took out 82 and 68 to lead 3-2 before Bunting hit top gear with legs of 15, 12, 14 and 13 darts as he stormed to victory.
Bunting will now play Jonny Clayton in Saturday's second round at the Victoria Stadium in a tasty tie as the seeded stars enter the event.
Galliano, meanwhile, will carry Gibraltarian hopes into round two following his 6-2 win over Mario Vandenbogaerde, as the 21-year-old enjoyed his first European Tour win.
Galliano had been due to work as a police officer on Saturday, but has been granted the day off to prepare for his dream tie with World Champion Peter Wright.
Four other Host Nation Qualifiers all suffered defeat on Friday, including 16-year-old debutant Dylan Duo Jnr and former World Cup representatives Dyson Parody, Manolo Vilerio and Sean Negrette.
Chris Dobey took a step towards Cazoo European Championship qualification by defeating debutant Duo Jnr 6-1, and he now plays Damon Heta on Saturday.
Experienced Parody - a former quarter-finalist in Gibraltar - lost out 6-4 to Ryan Joyce, while Vilerio was defeated 6-2 by Jason Lowe and Negrette picked up just one leg in his defeat to Kenny Neyens.
Gibraltar's Justin Hewitt withdrew from the event on Friday morning through illness, meaning that Steve Beaton received a Bye through to a second round tie with Michael van Gerwen.
Saturday's second round will also feature a repeat of the 2021 final between Gerwyn Price and Mensur Suljovic, after the Austrian produced a brilliant display to whitewash Keegan Brown on Friday.
Suljovic landed a perfect six doubles from as many attempts and averaged over 101 as he made an impressive return to action following a two-month break.
Ritchie Edhouse overcame John Henderson 6-4 with the aid of a 152 checkout in their opening leg, and he now plays Masters champion Joe Cullen in the last 32.
Emerging star Josh Rock sealed his place in the European Championship with a 6-4 defeat of Ryan Meikle as he moved through to meet former Gibraltar Darts Trophy winner Michael Smith.
Vincent van der Voort was another to put a foot into the European Championship by seeing off Martin Schindler 6-3, and he now plays World Grand Prix finalist Nathan Aspinall on Saturday.
William O'Connor boosted his hopes of qualifying for the European Championship with a 6-1 defeat of Jim Williams, which was sealed with a 125 checkout.
Germany's Gabriel Clemens came from a leg down against Adam Hunt to race to a 6-2 victory which means he now plays Dimitri Van den Bergh.
Wesley Plaisier continued his strong recent form with a 6-0 whitewash of Jeff Smith, while Rusty-Jake Rodriguez came through a last-leg decider with Marko Kantele.
Rowby-John Rodriguez matched his younger brother by landing a ten-darter in his 6-3 win over Keane Barry, with the Austrian also taking out 156 in setting up a tie with Jose de Sousa.
2022 Gibraltar Darts Trophy schedule and results
Friday October 14 - First Round results
Craig Galliano 6-2 Mario Vandenbogaerde
William O'Connor 6-1 Jim Williams
Jason Lowe 6-2 Manuel Vilerio
Kenny Neyens 6-1 Sean Negrette
Ritchie Edhouse 6-4 John Henderson
Wesley Plaisier 6-0 Jeff Smith
Rusty-Jake Rodriguez 6-5 Marko Kantele
Steve Beaton Bye (Justin Hewitt withdrew)
Rowby-John Rodriguez 6-3 Keane Barry
Ryan Joyce 6-4 Dyson Parody
Stephen Bunting 6-3 Daryl Gurney
Chris Dobey 6-1 Dylan Duo Jr
Josh Rock 6-4 Ryan Meikle
Vincent van der Voort 6-3 Martin Schindler
Mensur Suljovic 6-0 Keegan Brown
Gabriel Clemens 6-2 Adam Hunt
Saturday October 15 - second round
Rob Cross v Rusty-Jake Rodriguez
Ryan Searle v William O'Connor
Dave Chisnall v Wesley Plaisier
Dirk van Duijvenbode v Jason Lowe
Danny Noppert v Ryan Joyce
Jose de Sousa v Rowby-John Rodriguez
Damon Heta v Chris Dobey
Nathan Aspinall v Vincent van der Voort
Michael Smith v Josh Rock
Luke Humphries v Kenny Neyens
Peter Wright v Craig Galliano
Jonny Clayton v Stephen Bunting
Michael van Gerwen v Steve Beaton
Gerwyn Price v Mensur Suljovic
Dimitri Van den Bergh v Gabriel Clemens
Joe Cullen v Ritchie Edhouse