Van Veen has been tipped as a potential dark horse on the back of success this year, which has included the European Championship and a second World Youth Championship title.
'The Giant' had never won on the Alexandra Palace stage before tonight, but flexed his quality against Reyes – a Mediterranean qualifier from Tenerife, Spain.
"Finally across that line," Van Veen told Sky Sports, reflecting on his first win in London.
The last few years have been a massive struggle here on this stage but today I felt right at home. Luckily it paid off.
"Two years ago when I was 2-0 up against Man Lok Leung and he won 3-2. When Cristo took the third set I went, 'Oh no, don't go back to 2-2 and get nervy'.
"Luckily, in the last set at 2-1 down, I started playing well, so I'm very happy."
Double 16 showed some love to Van Veen in the first set, with the 22-year-old checking out on it twice to claim the opener, despite Reyes averaging a higher 96.21.
He then snagged a break in the second on double 13 after Reyes missed tops, which he then followed up with another double 16 finish to seal a 107-average set.
Reyes, though, continued to show fight as out of nowhere he took out a monster 167 on the bull, grabbed a break and then got rid of 80 to get a set on the board.
Van Veen responded in set four by wiping out 96 via double 18, but Reyes still wouldn't go away until the 10th seed eventually put the match to bed with yet another clinical double 16.
Former champ Cross wins opener
Cross made it through to the second round with a comprehensive 3-0 victory against tournament debutant Cor Dekker.
'Voltage' has been in indifferent form this year and will have been desperate to kick off his campaign on a positive note.
He did just that against Norway's Dekker, taking full control from the off and capped off the victory in style by reeling in the 'Big Fish' checkout of 170.
"I was a little bit edgy today," Cross told Sky Sports on stage.
"I thought I was going to come out and be brand new, but I wasn't. The finish with that one I've been doing all week and that's lovely.
"I'm really proud of myself."
Cross made a fast start by winning all three legs in the first set, taking the opener with an average of 98.02.
Dekker, though, sprang to life in the second and broke with a tidy 80 checkout until Cross hit back and forced a decider, which he claimed to open a 2-0 lead.
Some monumental pressure from Cross handed him a break to begin the third, allowing him to finish off eight on double two.
Dekker was gifted a chance on tops to break back but spurned his opportunity as Cross took his, before smashing a match-winning 170.
Smith crashes out
The first upset of the tournament took place in the evening's opener as 12th seed Ross Smith was bundled out by debutant Andreas Harrysson 3-2 in a thriller.
Smith looked in control at the midpoint but blew six match darts, which handed the bearded Swede the momentum to force a deciding set.
There was no looking back at that point for Harrysson, who nestled his dart on the double five bed to close out the biggest win of his career.
Fan favourite Ricky Evans beat the equally entertaining Man Lok Leung of Hong Kong 3-0 with a 92.26 average to book his place in round two.
Evans has emerged as an Ally Pally star over the years for his Christmas-themed outfits and walk-ons.
Despite fading slightly towards the end, 'Rapid' will be feeling festive after a solid display, highlighted by an excellent 134 checkout.
Australia's Damon Heta battled some late-game adversity in his 3-1 win against Ireland's Steve Lennon to conclude the evening session.
The 16th seed went slightly off the boil in the third set, but reset his focus to complete a victory containing three ton-plus finishes and had a 58 per cent double success rate.
Ryan Searle showcased his scoring power to sweep past Chris Landman 3-0 in straightforward fashion.
'Heavy Metal' averaged 93.29, including 102.68 in a competitive second set and notched five 180s to down the Dutchman.
Ian White progressed with a 3-2 win in a battle of seasoned players against Mervyn King, but 'Diamond' was made to work by the former semi-finalist.
King, 59, was back on the Ally Pally stage for the first time since 2023 and rallied from 2-0 down until falling to 55-year-old White in the deciding set.
Friday's first match saw Niels Zonneveld beat New Zealand qualifier Haupai Puha 3-0 to set up a round two clash against 2023 world champion Michael Smith.
Friday's 2026 PDC World Darts Championship results
Afternoon session
Niels Zonneveld 3-0 Haupai Puha
Evening session
Ross Smith 2-3 Andreas Harrysson
Gian van Veen 3-1 Cristo Reyes