Radoslav Batak put Montenegro ahead after 13 minutes at Podgorica City Stadium, but Georgia levelled in first-half stoppage time through Vladimir Dvalishvili. Delibasic found the net 12 minutes from time to secure Montenegro's first win of qualifying Group 8 and leave Georgia without a win at the bottom of the standings.
Montenegro had much of the possession in the first half and took the lead when Batak converted Nikola Drincic's free kick. The hosts went close to doubling their advantage after 36 minutes, but Stevan Jovetic's header was saved by Georgia goalkeeper Giorgi Lomaia.
The visitors equalised in stoppage time at the end of the first half following Georgi Merabishvili's free kick, with Dvalishvili finding the net with a deflected shot.
The replacement latched on to Jovetic's pass and put the ball beyond Lomaia to seal the win. It was an emotional triumph for Montenegro head coach Zoran Filipovic, who was on the sideline despite the death of his mother this morning.