Gurney, who won the Players Championship Finals last month, averaged over 100 in an impressive opening display, which included six 180s.
The number five seed will take on last year’s semi-finalist Jamie Lewis in the third round.
“I’ve watched a few players lose 2-0 leads so I was focused on making sure that didn’t happen,” said Gurney, whose recent Minehead triumph saw him claim his second televised PDC title – following his World Grand Prix glory in 2017.
“Winning the Players Championship has given me a little bit more confidence but I don’t let myself get carried away because that is in the past.
“I just take one game at a time. I don’t think about winning tournaments, just matches, and I’m happy that I’ve done that and gone through to the next round.”
Vincent van der Voort joined Gurney in the last 32 by dumping out Darren Webster in straight sets.
Van der Voort, who had beaten Lourence Ilagan on Monday, dumped out number 13 seed Webster, who only managed to win one leg.
“I didn’t play well but I played at little bit better than Darren,” said The Dutchman, who celebrated his birthday with the victory.
“All that mattered was getting through this match. It was difficult playing a day after winning the first match the before so I’m not really concerned about the performance – only the result.
“I will have to play better in the next round but the main thing is that I will be there.”
Back-to-back PDC Unicorn World Youth Champion Dimitri Van Den Bergh also enjoyed a 3-0 victory as he moved into the second round.
The Belgian star defeated American qualifier Chuck Puleo to set up a meeting with Welshman Jonny Clayton.
“It was a comfortable result but I didn’t feel too comfortable,” said Van Den Bergh, who lost a thrilling quarter-final showdown with eventual World Champion Rob Cross 12 months ago.
“Last year after losing to Rob I thought what if I had hit those doubles but that is the difference between being good and being brilliant – just those few millimetres.
“I know I will have to play better in the next round but I’m glad I got the job done.”
Dutch talent Ron Meulenkamp progressed to the second round with a comeback win over Brazil’s Diogo Portela.
Meulenkamp had to come from two sets behind after Portela made a flying start to the match, only to see his hopes slip away as the Dutchman’s eight maximums helped him turn the tie around.
Japanese star Seigo Asada came from two sets down to defeat Poland’s Krzysztof Ratajski in round one.
Ratajski, a winner of three PDC ProTour titles in 2018, had looked to be cruising into the third round until Asada won the deciding leg of the third set.
The Asian Tour number two went on to take the next to sets, sealing the win with a brilliant 11-darter.
Steve Lennon made light work of Australia’s James Bailey, who failed to win a set on his World Championship debut.
Emerging Irish ace Lennon won the first set 3-1 before edging the second in a last leg decider – and he also won the third set 3-1 to set up a second meeting with Alan Norris.
Austria’s Rowby-John Rodriguez tasted victory at Ally Pally for the first time in four attempts by defeating Ricky Evans.
The former PDC Unicorn World Youth Championship finalist claimed a 3-1 victory to move into round two, where he will face Spanish number one Cristo Reyes.
Former World Grand Prix and UK Open champion Robert Thornton was knocked out in the first round by Swedish debutant Daniel Larsson, who won 3-1 to set up a last 64 meeting with Kim Huybrechts.
The action continues on Wednesday across two sessions with the two remaining first-round ties before six round two matches.
The £2.5 million tournament is being broadcast live on the dedicated Sky Sports Darts channel from December 13-January 1 and worldwide through the PDC’s international broadcast partners.
Schedule of Play
Tuesday, December 18
Daniel Larsson 3-1 Robert Thornton (R1)
Rowby-John Rodriguez 3-1 Ricky Evans (R1)
Seigo Asada 3-2 Krzysztof Ratajski (R1)
Vincent van der Voort 3-0 Darren Webster (R2)
Steve Lennon 3-0 James Bailey (R1)
Ron Meulenkamp 3-2 Diogo Portela (R1)
Dimitri Van den Bergh 3-0 Chuck Puleo (R1)
Daryl Gurney 3-0 Ross Smith (R2)
Wednesday 19 December
Afternoon Session (1230)
Nathan Aspinall v Geert Nentjes (R1)
Jeffrey de Graaf v Noel Malicdem (R1)
Joe Cullen v Brendan Dolan (R2)
Kim Huybrechts v Daniel Larsson (R2)
Evening Session (1900)
James Wilson v William O’Connor (R2)
Simon Whitlock v Ryan Joyce (R2)
Michael Smith v Ron Meulenkamp (R2)
James Wade v Seigo Asada (R2)