(1) Background: Wine contains a variety of molecules with potential beneficial effects on human health. Our aim was to examine the wine components with high-resolution mass spectrometry including high-resolution tandem mass spectrometry in two wine types made from grapes with or without the fungus Botrytis cinerea, or “noble rot”. (2) For LC-MS/MS analysis, 12 wine samples (7 without and 5 with noble rotting) from 4 different wineries were used and wine components were identified and quantified. (3) Results: 288 molecules were identified in the wines and the amount of 169 molecules was statistically significantly different between the two wine types. A database search was carried out to find the molecules, which were examined in functional studies so far, with high emphasis on molecules with antiviral, anti-inflammatory and anticancer activities. (4) Conclusions: A comprehensive functional dataset related to identified wine components is also provided highlighting the importance of components with potential health benefits.