The visitors, who had previously lost to Cercle Brugge and Fiorentina in Europe, had the first chance of the second half when Ferguson pushed away Akolo's low free-kick from the edge of the area.
Larne rallied and put in a sustained period of pressure, but just could not create the chance or land the key final ball.
Csoboth, always lively down the left, fired a shot that was well blocked by Bolger, though play was brought back for a handball.
There was a scare when Gortler clipped a ball forward for Willem Geubbels, who looked second favourite for the ball, but it was missed by the onrushing Ferguson. Thankfully for Larne, a combination of Ferguson and Bolger recovered the situation.
The decisive goal came when Gortler found Christian Witzig out wide and the substitute played a ball across goal for Vandersmersch to fire home, despite the best efforts of home defender Levi Ives.
The wild celebrations from the visiting players and staff said everything about how hard Larne had pushed them.
With the wind in their sails, captain Bolger had to be alert to hack away Gortler's cross before Diaby headed narrowly wide from a corner.
Substitute Moustapha Cisse thought he had added a third in stoppage time when he raced through, rounded Ferguson and tucked home but the flag was up for offside.
The substitute then forced Ferguson into a strong save as the visitors started to run the clock down.
Larne are without a win midway through their maiden European campaign, and face trips to Olimpija in Slovenia and Belarus club Dinamo Minsk, before a final home match with Gent.