Purpose: Deep Neuroevolution (DNE) holds the promise of providing radiology artificial intelligence (AI) that performs well with small neural networks and small training sets. We seek to realize this potential via a proof-of-principle application to MRI brain sequence classification. Methods: We analyzed a training set of 20 patients, each with four sequences/weightings: T1, T1 post-contrast, T2, and T2-FLAIR. We trained the parameters of a relatively small convolutional neural network (CNN) as follows: First, we randomly mutated the CNN weights. We then measured the CNN training set accuracy, using the latter as the fitness evaluation metric. The fittest child CNNs were identified. We incorporated their mutations into the parent CNN. This selectively mutated parent became the next generation's parent CNN. We repeated this process for approximately 50,000 generations. Results: DNE achieved monotonic convergence to 100% training set accuracy. DNE also converged monotonically to 100% testing set accuracy. Conclusions: DNE can achieve perfect accuracy with small training sets and small CNNs. Particularly when combined with Deep Reinforcement Learning, DNE may provide a path forward in the quest to make radiology AI more human-like in its ability to learn. DNE may very well turn out to be a key component of the much-anticipated meta-learning regime of radiology AI algorithms that can adapt to new tasks and new image types, similar to human radiologists.