Clayton had earlier beaten Luke Littler 4-2 in the quarter-finals, while defending champion Stephen Bunting lost 4-3 in a thriller that went to the final leg.
Littler, who became the youngest world darts champion aged 17 last month, had lost just one leg in his two previous matches in the tournament.
Clayton was a big underdog against the teenager, but his heavy scoring and high-quality finishing enabled him to run out a worthy winner.
Littler had been imperious in Milton Keynes although Clayton had also impressed and broke the tournament record with his 112.77 average in the first round.
Clayton still averaged more than a ton in the quarters, even though his 103.96 and eight 180s were bettered by Littler’s 108.5 and nine maximums – but the Welshman was superior on the doubles.
‘The Ferret’ had a 60% checkout percentage to Littler’s 35% – and had three ton-plus finishes including a 128 and 138 when taking the opening set.
Littler, who turned 18 in January, went off the boil as Clayton took the next two sets to lead 3-1, and even though the world champion got back to 3-2 Clayton kept his nerve to book his spot in the semis.
“Obviously Luke didn’t play his A game, but it’s a battle and I got over the line,” said Clayton.
“He’s a cracking guy and great darts player with a great future. He’s given me a big lesson the last two games I played him, so I got one back.”
Bunting was looking to build on his Bahrain Masters triumph but missed three match darts in his defeat by Noppert.
