Sudan dyes are synthetic azo dyes used by industry in a variety of applications. Classified as carcinogenic, they are not allowed in foodstuffs; however, their presence as adulterants in food products has been regularly reported. Here, we describe an innovative screening method to detect Sudan I, II, III, and IV in tomato sauce, palm oil, and chilli powder. The method entails minimal sample preparation, completely avoiding the liquid chromatography phase, followed by detection and identification through atmospheric pressure chemical ionization time-of-flight mass spectrometry, in positive ionization mode. Analytes were efficiently identified and detected in samples, fortified both with individual analytes and with their mixture, with an error in mass identification less than 5 ppm. Limits of identification of the analytes in the fortified samples were 0.5 to 1 mg/kg, depending on the dye and matrix. The method had a linear range of 0.05 to 5 mg/kg and good linear relationships (R2 > 0.98). Repeatability was satisfactory, with a coefficient of variation lower than 20%. The method was applied to detect the dyes in real adulterated chilli samples, previously found positive by confirmatory high-performance liquid chromatography–mass spectrometry and ELISA, and in commercial products purchased from supermarkets. In all positive samples, analytes were correctly identified with an error in mass identification lower than 5 ppm, while none of the 45 commercial samples analyzed were found to be contaminated. The proposed new assay is sensitive, with a limit of identification, for all the three matrices, complying with the limits defined by the European Union (0.5 to 1 mg/kg) for analytical methods. Compared with conventional methods, the new assay is rapid and inexpensive and characterized by a high throughput; thus, it could be suitable as screening technique to identify Sudan dyes in adulterated food products.