The Argentinian was on court for more than two hours as he claimed a hard-fought 6-4 5-7 7-6 (8-6) triumph on the clay.
Big-serving American Isner was typically strong on serve but let his guard down just once in the first set, which proved significant.
After taking advantage of his only break in the opener, Delbonis was pegged back at the ATP 250 event.
The world number 45 was broken in the 11th game of the second set, after failing to take a match point in the previous game, with Isner duly holding serve to set up a thrilling decider.
And the third and final set well and truly went the distance, despite Isner claiming a 4-2 lead at one stage.
Delbonis showed excellent temperament to break Isner when the latter served for the match at 5-4 and another tie-break followed.
With momentum behind him, Delbonis claimed victory to book a last-four clash against Frenchman Gilles Simon.
Fourth seed Simon was rarely troubled in an easy 6-4 6-1 win over Argentina's Carlos Berlocq.
Defending champion Albert Montanes of Spain had to come from behind to defeat Argentine qualifier Leonardo Mayer 6-7 (6-8) 6-4 6-4.
Montanes eventually came through an epic tussle to keep his hopes of a repeat success alive.
He will meet second seed Ernests Gulbis in the other semi-final after the Latvian saw off Russian Dmitry Tursunov.
Gulbis smashed 18 aces in a 6-3 3-6 7-6 (7-5) victory as he moved a step closer to his second title of the year.