5G and Beyond 5G networks are calling for advanced networking schemes that can efficiently contribute to deal with the foreseen increase of the mobile data traffic, which inherently brings along an increase of the energy consumed by mobile nodes to support it. The non-real-time nature of an important share of that traffic makes it possible to use opportunistic networking mechanisms in cellular networks that can exploit the traffic’s delay-tolerance to find efficient transmission conditions. In this context, this paper proposes an scheduling and mode selection scheme that integrates opportunistic Device-to-Device (D2D) networking mechanisms in cellular networks to reduce the energy consumption for non-real-time traffic. The proposed scheme utilizes a probabilistic model that exploits context information available in cellular networks to obtain an a-priori estimate of the energy cost for transmitting the different fragments of a content using any of the following modes: single-hop traditional, opportunistic cellular and opportunistic D2D-aided cellular. Based on these estimates, the proposed scheme selects the communication mode for each fragment, and schedules the time instant at which the transmission should take place. Our performance evaluation shows that the proposed scheme results in up to 90% energy consumption reduction, compared to traditional single-hop cellular communications, and performs closely to an optimal scheme which assumes full knowledge of network conditions and nodes’ trajectories.