Oscillometric monitors are the most common automated blood pressure (BP) measurement devices used in non-specialist settings. However, their accuracy and reliability vary under different settings and for different age groups and health conditions. A main limitation of the existing oscillometric monitors is their underlying analysis algorithms that are unable to fully capture the BP information encoded in the pattern of the recorded oscillometric pulses. In this paper, we propose a new 2D oscillometric data representation that enables a full characterization of arterial system and empowers the application of deep learning to extract the most informative features correlated with BP. A hybrid convolutional-recurrent neural network was developed to capture the oscillometric pulses morphological information as well as their temporal evolution over the cuff deflation period from the 2D structure, and estimate BP. The performance of the proposed method was verified on three oscillometric databases collected from the wrist and upper arms of 245 individuals. It was found that it achieves a mean error and a standard deviation of error of as low as 0.08 mmHg and 2.4 mmHg in the estimation of systolic BP, and 0.04 mmHg and 2.2 mmHg in the estimation of diastolic BP, respectively. Our proposed method outperformed the state-of-the-art techniques and satisfied the current international standards for BP monitors by a wide margin. The proposed method shows promise toward robust and objective BP estimation in a variety of patients and monitoring situations.