Malik Binismaeil scored five minutes before the end of regulation time to give the Mediterranean Knights a slender advantage ahead of next week’s return fixture.
Desmond Ofei’s side showed resilience throughout the encounter despite playing much of the second half with 10 men following the dismissal of Dacosta Antwi.
Ghana had an opportunity to take the lead in the first half when Daniel Adu-Adjei was released through on goal by an incisive pass, but his effort was denied by Libya goalkeeper Mohammed Ammar.
The Black Meteors remained disciplined after going down to 10 men, holding off the hosts for much of the second half and appearing set to secure a valuable draw.
However, Binismaeil found the breakthrough in the closing stages to hand Libya the first-leg victory.
Ghana will now need to overturn the one-goal deficit when the two sides meet again at the Accra Sports Stadium on Tuesday, with a place in the final qualifying round at stake.
The winner of the tie will face Niger in the final qualifying round after Equatorial Guinea withdrew from the competition.
The Black Meteors are seeking to secure a place at the 2027 U-23 AFCON in Egypt, which will also serve as the qualification tournament for the 2028 Olympic Games.
