We report on the observation of bright emission of single photons under pulsed resonance fluorescence conditions from a single quantum dot (QD) in a micropillar cavity. The brightness of the QD fluorescence is greatly enhanced via the coupling to the fundamental mode of a micropillar, allowing us to determine a single photon extraction efficiency of (20.7 ± 0.8) % per linear polarization basis. This yields an overall extraction efficiency of (41.4 ± 1.5) % in our device. We observe the first Rabi-oscillation in a weakly coupled quantum dot-micropillar system under coherent pulsed optical excitation, which enables us to deterministically populate the excited QD state. In this configuration, we probe the single photon statistics of the device yielding g(2)(0) = 0.072 ± 0.011 at a QD-cavity detuning of 75 μeV.