Wildcard Ruud, playing in his maiden ATP semi-final at the age of 18, broke his opponent twice to win the opener but Carreno Busta battled back to level up the match in a topsy-turvy second set before easing through the decider 6-0.
The world number 24 will face Dominic Thiem in Sunday's final after the Austrian second seed, who has yet to lose a set in the tournament, stormed past Albert Ramos-Vinolas 6-1 6-4 in the other semi.
Spaniard Ramos-Vinolas briefly looked like he might muster a comeback when he broke serve to level the scores at 4-4 in the second but Thiem, the world number eight, broke back before serving out for the match.
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(Writing by Andrew Downie, editing by Nick Mulvenney)
