A computed tomography (CT) scan is an important radiological imaging method in diagnosing pneumonia caused by SARS-CoV-2. Within the scope of the study, three classes of automatic classification–COVID-19 pneumonia, healthy, and other pneumonia–were carried out. Using deep learning as a classifier, a total of 6,377 CT images were used, including 3,364 COVID-19 pneumonia, 1,766 healthy, and 1,247 other pneumonia images. A total of seven architectures, including the most recent convolutional neural network (CNN) architectures, MobileNetV2, ResNet-101, Xception, Inceptionv3, GoogLeNet, EfficientNetB0, and DenseNet201, were used in the study. The classification results were obtained using the CT images, and they were calculated using the feature images obtained by applying local binary patterns on the CT images. The results were then combined with the help of a pipeline algorithm. The results revealed that the best overall accuracy result obtained by using CNN architectures could be improved by 4.87% with a two-step pipeline algorithm. In addition, significant improvements were achieved in all other measurement parameters within the scope of the study. At the end of the study, the highest sensitivity, specificity, accuracy, F-1 score, and Area under the Receiver Operating Characteristic Curve (AUC) values obtained for the COVID-19 pneumonia class were 0.9004, 0.8901, 0.8956, 0.9010, and 0.9600, respectively. The highest overall accuracy value was 0.8332. The most important output of the work carried out is the demonstration that the results obtained with the most successful CNN architectures used in previous studies can be significantly improved thanks to pipeline algorithms.