It did not take long for Filip Djordjevic's first effort on the home goal, but his second-minute shot was slashed high and wide from an angle in the box.
Fernando Aristeguieta was the next player to have a sight of goal for Nantes, but he put his effort wide when well placed.
The hosts started to come into the game and came close through Lionel Mathis's fizzing effort that skidded just wide.
In an end-to-end game the first goal was becoming ever more crucial and it finally came after 63 minutes as Younousse Sankhare thumped in a header from close range.
The visitors came again after the goal but Guingamp remained strong and were able to hold on for three big points.