The UK Open champion beat Dirk van Duijvenbode in Friday night’s opener before Price came through a classic to continue his tilt for World Matchplay glory.
Price and De Sousa traded 160 checkouts in an explosive start but it was the Welshman who boasted the slender advantage, leading 3-2 with a 105 average.
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He was outscoring the Portuguese star, a pattern that continued in the second session, but a two-dart 93 combination from De Sousa saw him level at 5-5 despite a 12-point disparity in the averages.
Price’s pressure paid dividends in leg 12 as he finally established some daylight, yet De Sousa delivered an emphatic riposte by taking out a spectacular 90 finish with successive double 18s.
The Welshman responded with a third consecutive break to open up a three-leg gap before extending his cushion to 13-8.
Price appeared to be cruising through but De Sousa had other ideas, producing a remarkable five-leg burst to level up proceedings.
The second seed stopped the rot with consecutive 14-darters to move one leg away from victory, only for De Sousa to conjure up a sublime 10-dart skin saver to prolong the tussle.
Nevertheless, he squandered five darts at a double to force a tie-break, enabling Price to wrap up a famous victory which means he will leapfrog Peter Wright to become world number one once the tournament is over.
Earlier in the night, Noppert turned on the style in the latter stages to record a 16-11 victory over van Duijvenbode.
The UK Open champion was below-par in the first half of the match but delivered the goods late on, landing 10 180s and producing two ton-plus finishes.
Despite converting a superb 132 finish on the bull, Van Duijvenbode endured a torrid start on the outer ring, converting one of his first 13 attempts at double as Noppert established a 4-1 cushion.
However, Noppert was struggling in the scoring department and Van Duijvenbode took control midway through the contest, winning five out of six legs to move 8-7 ahead.
The former World Grand Prix runner-up threatened to run away with the contest until Noppert landed a 150 checkout to lead 9-8, which provided the catalyst for his revival.
Noppert began to find the treble 20 with greater regularity and opened up a 12-9 lead courtesy of a clinical 87 finish, only for Van Duijvenbode to hit back with a 116 outshot to keep his hopes alive.
Van Duijvenbode reduced the arrears to 12-11 with a nerveless 63 checkout but Noppert restored his two-leg buffer before punishing a costly missed big number by his compatriot to move two legs away.
The 31-year-old cemented his advantage with a ninth 180 and a 14-dart hold, before producing a delightful 121 finish on the bull to seal his progression in style.
Price and Noppert meet in tonight’s first semi-final before Michael van Gerwen faces Dimitri Van den Bergh in the second match.