Nadal managed to make his mark in the early stages of the match, snatching the first break of serve, which unnerved his Colombian opponent.
The initial break set the tone for the rest of the set, where Nadal powered some impressive shots across the court to take the lead in Barcelona.
Despite a disappointing effort in the opening set, 24-year-old Farah managed to stay composed and hold his serve in an attempt to push back the Spaniard.
While Farah attempted to force through a comeback, Nadal was too much for the Colombian and managed to book his spot in the quarter-finals.
The Spaniard will take on Janko Tipsarevic for a place in the semi-finals of the tournament.