In a frenetic opening 15 minutes, the visitors found themselves three goals to the good as Andre-Pierre Gignac strike and new signing Dimitri Payet (twice) benefited from some shambolic defending and goalkeeping.
Guingamp managed to pull a goal back through Mustapha Yatabare in the final quarter of the match but it was too little too late, with the same player having earlier missed a penalty.
Fabrizio Ravanelli's first competitive game in charge of Ajaccio ended in defeat as St Etienne ran out 1-0 winners at the Stade Francois Coty.
Brandao's first-half strike in the searing Corsican sunshine was enough to secure all three points for Les Verts as the hosts struggled to offer a response and finished the game with 10 men.
St Etienne made the breakthrough thanks to good work from Romain Hamouma, the winger showing great control before squaring for Brandao to tap home.
Having already been booked in the first half, Benjamin Andre showed naivety with a silly challenge from behind on Benjamin Corgnet and the hosts were forced to see out the few remaining minutes a man down.