We present flight results from the optical pointing control system onboard the Planetary Imaging Concept Testbed Using a Rocket Experiment (PICTURE) sounding rocket. PICTURE (NASA mission number: 36.225 UG) was launched on 8 October 2011, from White Sands Missile Range. It attempted to directly image the exozodiacal dust disk of $ϵ$ Eridani (K2V, 3.22 pc) down to an inner radius of 1.5 AU using a visible nulling coronagraph. The rocket attitude control system (ACS) provided 627 milliarcsecond (mas) RMS body pointing ($\sim 2^{\prime \prime }$ peak-to-valley). The PICTURE fine pointing system (FPS) successfully stabilized the telescope beam to 5.1 mas ($0.02\lambda /D$) RMS using an angle tracker camera and fast steering mirror. This level of pointing stability is comparable to that of the Hubble Space Telescope. We present the hardware design of the FPS, a description of the limiting noise sources and a power spectral density analysis of the FPS and rocket ACS in-flight performance.