Northern Ireland’s Gurney beat Ronny Huybrechts of Belgium 3-1, while fifth-seeded Austrian Suljovic saw off Kevin Painter, comfortably defeating the Englishman 3-0.
Gurney.
The World number four from Londonderry hit seven perfect darts in the opening leg but missed out on a nine-darter.
Gurney edged a high quality first set 3-2 and won the next 3-0 before his Belgian opponent took the third 3-1.
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A 170 checkout helped the impressive Gurney, who averaged over 100, to win the fourth set 3-0.
Gurney has genuine title hopes at Alexandra Palace after winning the World Grand Prix title in Dublin in October.
The 31-year-old reached the quarter-finals at last season’s PDC World Championships and also progressed to the semi-finals at the UK Open and the World Matchplay.
Gurney will take on John Henderson or Marko Kantele in the second round.
“I played really well in the first two sets but tried too hard at times in the third,” Gurney told Sky Sports.
“I was lucky to get the 170 but to get the win is the important thing.
“I need to play like I did in the first sets all the time to progress in this competition.”
Suljovic, who faces Scot Robert Thornton in round two, was quoted on www.pdc.tv as saying: “Kevin beat me before and I told him on the stage that’s 1-1 now so it’s a good feeling, it’s brilliant.
“I’m happy I’m here, this is brilliant playing on that stage with this crowd. It’s amazing.”