The Spaniard struggled to find his feet in the early stages of the first set by losing his service game, but the 26-year-old was able to break back in order to prevent Paire from taking control.
While Nadal's strong shots across the court proved damaging, Paire was able to hold his serve and push his Spanish opponent to a tie-break to decide the lead.
Despite impressing throughout the opening exchanges, Paire could only get two points on the board in the tie-break, resulting in him relinquishing the first set.
Games continued to go by the way of serve in the second set until Nadal moved up a gear to secure a vital break of serve, which Paire was unable to get back from.
Despite a battling start, Nadal eventually moved into the quarter-finals by comfortably snatching the final few games in the second set.