The progress in the field of neural computation hinges on the use of hardware more efficient than the conventional microprocessors. Recent works have shown that mixed-signal integrated memristive circuits, especially their passive (0T1R) variety, may increase the neuromorphic network performance dramatically, leaving far behind their digital counterparts. The major obstacle, however, is immature memristor technology so that only limited functionality has been reported. Here we demonstrate operation of one-hidden layer perceptron classifier entirely in the mixed-signal integrated hardware, comprised of two passive 20 × 20 metal-oxide memristive crossbar arrays, board-integrated with discrete conventional components. The demonstrated network, whose hardware complexity is almost 10× higher as compared to previously reported functional classifier circuits based on passive memristive crossbars, achieves classification fidelity within 3% of that obtained in simulations, when using ex-situ training. The successful demonstration was facilitated by improvements in fabrication technology of memristors, specifically by lowering variations in their I-V characteristics.