Unstoppable Djokovic is now just three wins short of matching Guillermo Vilas's record of 46 consecutive wins and one shy of John McEnroe's mark of 42 for an unbeaten start to a season set in 1984.
The red-hot Serb breezed to his fifth career win in six meetings against the 13th-seeded Gasquet.
"I'm happy with my game. I played a great match against a great player, but I got important breaks and made no mistakes after that," said Djokovic.
"I'm playing the best tennis of my life at the moment. But it's important to just focus on each match and see how far I can go," he added.
Third seed Federer has reached the last eight without dropping a set as he continues to thrive at a Roland Garros tournament where the world's top two, Rafael Nadal and Djokovic, are expected to reach the final.
PTI
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