The opening day of the event delivered 32 first-round ties across the main and second stages in a marathon session, with Van Veen edging Humphries in a deciding-leg thriller - a repeat of last month’s European Championship final.
Humphries surged into a 3-0 lead before Van Veen, galvanised by a superb 161 checkout, reeled off five of the next six legs to move 5-4 ahead.
Although the 23-year-old Dutchman squandered two match darts in the 10th, he held his nerve in the decider to seal a fourth straight win over the world champion.
New world No. 1 Littler, meanwhile, averaged 104.46 in a dominant 6-1 win over Sweden's Jeffrey de Graaf, landing six doubles from eight attempts and closing out the match with three consecutive 14-darters.
“It felt amazing being introduced as the world number one,” said the 18-year-old, chasing a sixth televised ranking title of the season. “It’s probably one of the best feelings I’ve had in my career, and hopefully there’s more to come.”
Top seed Gerwyn Price opened with a convincing 6-2 victory against Max Hopp, highlighted by a 154 checkout, though fellow seed Wessel Nijman departed after a deciding-leg defeat by compatriot Richard Veenstra despite averaging 102.41 and hitting five maximums.
Former finalists Jonny Clayton, Rob Cross and Dave Chisnall were also sent packing, beaten by James Hurrell, Sebastian Bialecki and Ryan Joyce, respectively.
Joyce now meets sixth seed Jermaine Wattimena, who averaged almost 102 in his all-Dutch win over Wesley Plaisier.
World No. 4 Stephen Bunting and 2018 champion Daryl Gurney set up a second-round meeting following routine wins against Ritchie Edhouse and Brendan Dolan.
Gurney is one of three former champions still standing in Minehead, alongside Gary Anderson and Peter Wright, who have also progressed.
Anderson, Scotland's No. 1, dispatched Belgian Mario Vandenbogaerde 6-2 to book a tie with Ricardo Pietreczko, after the German No. 2 extended William O’Connor’s run of first-round exits at this tournament, while Wright beat Joe Cullen 6-3 to earn a heavyweight meeting with James Wade, who saw off Mickey Mansell by the same score.
Danny Noppert continued his fine form, averaging 103.84 in a victory over Ricky Evans to set up a clash with Madars Razma, who defeated Dirk van Duijvenbode 6-3.
Germany’s No. 1 Martin Schindler overcame former world champion Michael Smith, while Josh Rock progressed with a routine 6-3 win against Gabriel Clemens.
Nathan Aspinall thrilled the Somerset crowd with a 170 finish during his 6-3 win over Czech No. 1 Karel Sedlacek in a contest featuring eight maximums. Kevin Doets also produced a 170 in his defeat to Callan Rydz, who moves on to face 2021 runner-up Ryan Searle.
Searle was clinical on the doubles in his 6-1 victory over Darren Beveridge, after fourth seed Ross Smith eased past Ryan Meikle by the same score to set up an eye-catching clash with Littler.
Andrew Gilding survived nine match darts as he overturned a 5-3 deficit against Dom Taylor; he now faces Justin Hood, who knocked out third seed Damon Heta on debut.
Another debutant, Cam Crabtree, rallied from 4-1 down to beat Mike De Decker and earn a meeting with fifth seed Chris Dobey, as 'Hollywood' thrashed Keane Barry 6-1 in Friday’s finale.
Elsewhere, Krzysztof Ratajski ground out a scrappy win over Raymond van Barneveld and will now meet Van Veen for a place in round three.
Bradley Brooks and Adam Lipscombe also advanced with 6-1 victories against Martin Lukeman and Cameron Menzies.
Scott Williams, Luke Woodhouse and Nick Kenny completed the round-two line-up with victories over Ian White, Alan Soutar and Niels Zonneveld, respectively.
Round two continues across both stages on Saturday afternoon, followed by round three later in the evening as the stage two action draws to a close.
Results
Sebastian Bialecki 6-2 Rob Cross
Ryan Joyce 6-4 Dave Chisnall
Cam Crabtree 6-5 Mike De Decker
Danny Noppert 6-2 Ricky Evans
James Wade 6-3 Mickey Mansell
James Hurrell 6-3 Jonny Clayton
Ross Smith 6-1 Ryan Meikle
Bradley Brooks 6-1 Martin Lukeman
Andrew Gilding 6-5 Dom Taylor
Scott Williams 6-2 Ian White
Nick Kenny 6-4 Niels Zonneveld
Callan Rydz 6-4 Kevin Doets
Adam Lipscombe 6-1 Cameron Menzies
Daryl Gurney 6-3 Brendan Dolan
Luke Woodhouse 6-2 Alan Soutar
Ricardo Pietreczko 6-3 William O'Connor
Martin Schindler 6-4 Michael Smith
Josh Rock 6-3 Gabriel Clemens
Gerwyn Price 6-2 Max Hopp
Stephen Bunting 6-2 Ritchie Edhouse
Luke Littler 6-1 Jeffrey de Graaf
Gian van Veen 6-5 Luke Humphries
Nathan Aspinall 6-3 Karel Sedlacek
Chris Dobey 6-1 Keane Barry
Jermaine Wattimena 6-3 Wesley Plaisier
Ryan Searle 6-1 Darren Beveridge
Richard Veenstra 6-5 Wessel Nijman
Krzysztof Ratajski 6-3 Raymond van Barneveld
Madars Razma 6-3 Dirk van Duijvenbode
Gary Anderson 6-2 Mario Vandenbogaerde
Peter Wright 6-3 Joe Cullen
Justin Hood 6-4 Damon Heta