Acute stress is a physiological condition that may induce several neural dysfunctions with a significant impact on life quality. Accordingly, it would be important to monitor stress in everyday life unobtrusively and inexpensively. In this paper, we presented a new methodological pipeline to recognize acute stress conditions using electrodermal activity (EDA) exclusively. Particularly, we combined a rigorous and robust model (cvxEDA) for EDA processing and decomposition, with an algorithm based on a support vector machine to classify the stress state at a singlesubject level. Indeed, our method, based on a single sensor, is robust to noise, applies a rigorous phasic decomposition, and implements an unbiased multiclass classification. To this end, we analyzed the EDA of 65 volunteers subjected to different acute stress stimuli induced by a modified version of the Trier Social Stress Test. Our results show that stress is successfully detected with an average accuracy of 94.62%. Besides, we proposed a further 4-class pattern recognition system able to distinguish between non-stress condition and three different stressful stimuli achieving an average accuracy as high as 75.00%. These results, obtained under controlled conditions, are the first step towards applications in ecological scenarios.