The Atletico Madrid midfielder struck three terrific goals after the interval to see Spain through to Friday's showpiece, with Roberto Gagliardini having seen red.
Following a quiet first half all four goals and Gagliardini's dismissal came in the space of 21 explosive second-half minutes, Spain's quality shining through to down the depleted Italians.
Gerard Deulofeu should have opened the scoring after 30 minutes but he fired wide at the back post after being found by a clever lofted Dani Ceballos pass.
The opener arrived six minutes into the second half, Saul collecting from Ceballos and bending a superb strike into Gianluigi Donnarumma's bottom-right corner.
Italy's hopes were seemingly dealt a decisive blow soon afterwards when Gagliardini was dismissed for a second yellow card after a late tackle on Ceballos.
The 10 men roared back after 61 minutes, however, with Federico Bernardeschi holding off a series of challenges and finishing via the aid of a small deflection.
But within three minutes Spain were back in front after Donnarumma was beaten again, Saul smashing home a brilliant left-footed finish from 30 yards.
Marco Asensio scored a hat-trick against Macedonia in Spain's opening group game and the Real Madrid starlet provided the assist for Saul's third goal.
The cutback from the left flank was perfectly weighted for Saul to hit a sweet first-time strike into Donnarumma's bottom-left corner, ensuring Spain will play Germany in Krakow in Friday's final.