Quantum dots (QDs) are an excellent single-photon source that can be combined with a spin quantum memory. Many quantum technologies require increased control over the characteristics of emitted photons. A powerful approach is to trigger coherent Raman photons from QDs with a Λ energy-level system, such as the spin singlet-triplet system in two coupled QDs. The temporal and spectral behavior of single Raman photons can be varied simply by modifying the excitation source. Here, we demonstrate control of the single-photon pulse shape in a solid-state system on a timescale much shorter than the radiative lifetime, in addition to control of the frequency and bandwidth. We achieve a photon pulse width of 80 ps-an order of magnitude shorter than the exciton lifetime. Possible applications include time-bin encoding of quantum information, matching photons from different sources, and efficient single-photon transfer in a quantum network.