Despite the efficacy of strong emission control plans that have been implemented the last few decades, polychlorinated dibenzo-p-dioxins (PCDDs) and polychlorinated dibenzofurans (PCDFs) may still be released from anthropogenic sources such as sinter plants, and municipal and hazardous waste incinerators. Monitoring for PCDDs and PCDFs in gaseous emissions from such facilities is important due to the acute toxicity of these compounds even at trace levels. Currently, most of these samples from the African continent are being analysed abroad at high cost, with the direct consequence that the number of measurements are kept to a minimum. In this context, we developed a more affordable analytical approach for the measurement of PCDD/Fs sampled onto Amberlite XAD-2 sorbent, which relies on a novel extraction, clean-up, and analysis method with the aim of reducing both the cost and the complexity of standard methods while maintaining high quality results. A simple, sequential, three-hour end-over-end tumbling extraction procedure was developed employing acetone: n-hexane (1:9) as extraction solvent. This was combined with a dimethyl sulfoxide (DMSO) clean-up to remove aliphatic interferences, prior to direct analysis by gas chromatography triple quadrupole mass spectrometry. The Unites States Environmental Protection Agency Method 23, in contrast, requires a 16-hour Soxhlet extraction with toluene and multiple column chromatography steps. The end-over-end tumbling extraction yielded an average recovery of 79% for PCDD/Fs usually monitored in gaseous samples, whilst an average recovery of 89% was achieved for the DMSO clean-up procedure. In addition, an overall average recovery of 78% and a Z-score of -1.1 was obtained using the developed method for the proficiency testing of a solid reference material, proving the method is fit for purpose. It was then successfully applied to the analysis of air emissions from a medical waste incinerator, which further showed that the alternative approach may deliver quality, fast, and cost-effective analysis of gaseous PCDD/Fs sampled onto Amberlite XAD-2 sorbent in a developing country context.