Welshman Clayton proved too strong, defeating the Dutch darting legend 10-7 on the opening night.
Nathan Aspinall, who won the tournament last year, narrowly advanced to the second round with a nervy 10-8 win against Luke Woodhouse.
World number one Luke Humphries continued his stellar 2024, winning his match with an average of over 108.
Catch up on all the action from day one of the World Matchplay:
Price (#4) 10-4 Gurney (#27)
Gerwyn Price started the match sloppily, as he had a chance for the break from 116. He only threw a double 19 with his second arrow instead of a single, and as a result, he did not get an arrow on the break.
Daryl Gurney took advantage and made it 1-0. In the third leg, Price did get a break after winning his own leg. The 50 went out for a 2-1 lead. He also grabbed the double break in the fifth leg by cleverly throwing out 130. Thus, Price went into the break 4-1.
After the break, Price opened with a maximum score, the second of the match. Gurney did get an immediate chance at the break from 68 but missed. So did Price from 75 and so Gurney came back a break anyway: 4-2.
Gurney only failed to cash in on the break as he failed to throw out 124. Price did throw tops and took another double break lead. It rained breaks, as the fourth in a row followed in the eighth leg. Gurney threw out double six. He then won his leg and had two chances to move to 5-5, but missed two chances on double 8. Price did throw out tops and was ahead 6-4.
Price rock solid in the end
Price hurt Gurney by breaking even in the 11th leg. Tops made it 7-4.
Also in the thirteenth leg, Price took the break by hitting 108 to make it 9-4, match point. He won the match by throwing out 47. So it became 10-4 and Price goes to the next round.
Clayton (#8) 10-7 Van Barneveld (#29)
Van Barneveld was hit right away in the first leg, as Clayton threw out 106 and took the break in the first leg.
The Dutchman had a chance for the rebreak in the second leg, but missed tops from 105. Clayton hit double 6 to lead 2-0. In the fourth leg, Van Barneveld did get the break via double 6 to make it 2-2.
He found the triples a lot easier than Clayton in the early stages. But Clayton did go into the first break with a lead, as he grabbed his second break by throwing out double 12: 3-2.
Immediately after the break, Clayton had three chances at the break, but missed. Van Barneveld hit double 10 to come back to 4-3.
Van Barneveld did get into trouble after that, as in leg nine the break did come via 48. That made it 6-3. He had a chance for the break on 135, but missed the bullseye and saw Clayton throw out again via 48: 7-3 at the second break.
Clayton punishes everything
Van Barneveld responded at the start of the third session and came back to 7-5 by throwing out 72. In the 13th leg, Barney threw 140 three times but did give up two chances for a break. Clayton missed double 18 twice, making it 7-6 after all. Van Barneveld hit double 10 and was back in the match.
But he then gave that away. Clayton dealt a blow and took the break via 35, 9-6 and match point. On 87, Clayton got a match dart but missed the bullseye. Van Barneveld grabbed the final straw by throwing double 6 to post a break back: 9-7.
Clayton eventually did win the match as he grabbed the break in the last leg. Via double 16, it was 10-7 for the Welshmen.
Humphries (#1) 10-3 Pietreczko (#33)
Luke Humphries started the match well, quickly leading 2-0. He took the break after just one leg by throwing out tops and then kept his own leg by throwing out 68 in two darts.
Humphries also broke in the third leg. He threw 180 to leave double 15 and that hit: 3-0. He also won the fourth leg, but it did not become 5-0 at the break. Ricardo Pietreczko threw out double 14 for the 4-1.
Humphries unstoppable
In the second session, there were no breaks, and it was 7-3 at the break. The level was very high. Pietreczko threw 103.58 on average but still could not make it very difficult for Humphries.
The Englishman threw over 107 on average and threw his doubles well, 53.85 per cent.
In the third session, Humphries came out of the dressing room again and grabbed the break. He got his first match dart at 9-3, but missed the double 8.
The German threw out 44 and made it 9-4, but could not prevent it becoming 10-4 after that. Humphries finished on a great average, 108.76.
Nathan Aspinall (#5) 10-8 Luke Woodhouse (#34)
Aspinall indicated to Viaplay before the match that his injury was so bad that he would have surgery on Friday, playing with a taped forearm.
He escaped in the first leg, as Woodhouse had four chances at the break. He missed them all and so it was 1-0 for the reigning champion. In the third leg, he did grab that break and led 2-1. But the rebreak came just one leg later as Aspinall threw out 128.
In the fifth leg came a third break in a row and so Woodhouse went into the first break with a 3-2 lead.
In the second session too, despite six chances, Woodhouse failed to cash in on his break.
Aspinall made it 3-3 as a result and stayed in the match. Woodhouse lost his momentum and was looking at a 5-3 deficit after eight legs. Aspinall grabbed the break by throwing out 81. In the end, both players left the stage with a 6-4 score in favour of The Asp.
Aspinall fights and wins
Woodhouse grabbed a break right away in the first leg of the third session and made it 6-5 via tops. Aspinall had three chances to take back the break in the 12th leg, but he failed to get 40 out. Woodhouse threw double 10 and levelled the score: 6-6.
Aspinall won the 13th leg and posted a very important break in the 14th. Two 180s helped make it 8-6. Woodhouse stayed in the match as he threw out 80 and grabbed the break back: 8-7.
Woodhouse missed a crucial double at 8-8. He missed double 12 for a 138 finish and saw Aspinall throw out 60: 9-8 and match point for the world number 5.
Woodhouse again succumbed to the pressure and did not yield in the final leg. Aspinall won 10-8 by hitting double 16.