Performance degradation is, in general, regarded as a power quality problem. One solution to recover grid performance is through the application of a unified power quality conditioner (UPQC). Although these devices are multi-input/multi-output (MIMO) systems, the most common control strategies consist of two decoupled controllers, which neglect the coupling effects and add uncertainty to the system. For this reason, this paper proposes a multivariable resonant observer-based control strategy of a UPQC system. This method includes all significant coupling effects between this system and the grid. This strategy results in a stability-based compensator, which differs from recently proposed strategies that are based on signal calculation and cannot assure closed-loop stability. In addition, this paper introduces a simplified controller tuning strategy based on optimal conventional methods without losing closed-loop performance. It implies that the controller can be easily tuned, despite the complexity of the MIMO dynamic model. The UPQC with the resonant observer is verified on an experimental setup for a single-phase system, obtaining three relevant results for power quality improvement: (1) harmonics compensation tested with a total harmonic distortion limit of 5%; (2) sags and swells mitigation; and (3) power factor correction, achieving a unitary value on the grid side.