Neurophysiological and psychological models posit that emotions depend on connections across widespread corticolimbic circuits. While previous studies using pattern recognition on neuroimaging data have shown differences between various discrete emotions in brain activity patterns, less is known about the differences in functional connectivity. Thus, we employed multivariate pattern analysis on functional magnetic resonance imaging data (i) to develop a pipeline for applying pattern recognition in functional connectivity data, and (ii) to test whether connectivity signatures differ across emotions. Six emotions (anger, fear, disgust, happiness, sadness, and surprise) and a neutral state were induced in 16 participants using one-minute-long emotional narratives with natural prosody while brain activity was measured with functional magnetic resonance imaging (fMRI). We computed emotion-wise connectivity matrices both for whole-brain connections and for 10 previously defined functionally connected brain subnetworks, and trained an across-participant classifier to categorize the emotional states based on whole-brain data and for each subnetwork separately. The whole-brain classifier performed above chance level with all emotions except sadness, suggesting that different emotions are characterized by differences in large-scale connectivity patterns. When focusing on the connectivity within the 10 subnetworks, classification was successful within the default mode system and for all emotions. We conclude that functional connectivity patterns consistently differ across different emotions particularly within the default mode system.