Goualy Magique conjured the deciding goal in the 18th minute, as Academica boss Sergio Conceicao got one over his former club.
Magique was sent through on goal by a pin-point Ivanildo pass, before gratefully stabbing beyond Vid Belec.
The visitors did just enough to edge a tight encounter that featured few clear-cut goalscoring opportunities.
Academica had suffered a dreadful start to the season, winning just one of their opening seven matches, but now sit 11th having picked up two victories in three outings.
Olhanense, meanwhile, have just one victory from their last seven league games and will be eager to experience a swift change in fortunes as they bid to stave off the threat of relegation.
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