An analytical method for the identification and quantification of 10 different isocyanates and 11 different amines in polyurethane (PUR) foam and PUR-coated products was developed and optimized. Isocyanates were extracted and derivatized with di-n-butylamine, while amines were extracted with methanol. Quantification was subsequently performed by liquid chromatography–tandem mass spectrometry. Using this methodology, residual levels of isocyanates and amines in commercial PUR products were quantified. Although the recoveries of certain isocyanates and amines were low, the main compounds used as monomers in the production of PUR products, and their decomposition species, were clearly identified at quantifiable levels. 2,4- and 2,6-toluenediisocyanate were detected in most PUR foam samples and a pastry bag in the range of 0.02–0.92 mg/kg, with their decomposition compounds, 2,4- and 2,6-toluenediamine, detected in all PUR foam samples in the range of 9.5–59 mg/kg. PUR-coated gloves are manufactured using 4,4′-methylenebisphenyl diisocyanate as the main raw material, and a large amount of this compound, in addition to 4,4′-methylenedianiline and dicyclohexylmethane-4,4′-diamine were found in these samples.