Frank Farina's men secured the point necessary to seal their progress to the latter stages, as Terry Antonis's first-half strike was canceled out by Rostyn Griffiths, before Richard Garcia struck the winner with seconds remaining.
The Sky Blues, who needed to avoid defeat by a margin of two goals or more, took a big step toward the finals on 37 minutes through Antonis.
The Australia international ran on to captain Alessandro Del Piero's layoff before firing a low first-time shot beyond Jack Duncan from 25 yards.
It was not enough to secure a half-time lead, though, as the visitors hit back moments before the break through Griffiths, who capitalised on a hashed punch-out from goalkeeper Vedran Janjetovic to tap home at the back post.
With a place in the finals beckoning for Farina's men, Garcia made sure of the passage in the closing stages by scoring beyond Duncan.