The "King of Clay" needed nearly two hours to defeat the Frenchman for the 16th time in as many career matches, extending his set winning streak at Roland Garros to 34, reports Efe.
Sweden's Bjoren Borg holds the record for most consecutive sets won at the French Open, with 41 sets between 1979 and 1981.
Nadal's current streak dates back to the start of the 2016 tournament, when he was forced to withdraw due to a wrist injury prior to his third-round match.
The ten-time French Open champion ruthlessly took a 4-0 lead in the first set without dropping a single point.
However, things got complicated at 5-0 as Gasquet won three games in a row, a service break included, but world No. 1 Nadal halted his opponent's revival in the next game.
Nadal was then untouchable on serve during the next two sets, with his serve never once in danger, while he broke his rival's serve two times in each set.
The decisive factors in the match were Gasquet's unforced backhand errors and the 37 winners Nadal hit, nearly double what the Frenchman fired, as well as Nadal's efficacy while approaching the net (85 percent).
Nadal, whose birthday is on Sunday, is to play his 40th career round-of-16 match at a major against Germany's Maximilian Marterer, who defeated Estonia's Jurgen Zopp 6-2, 6-1, 6-4.
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