The world No.1, who is undefeated at Roland Garros since his only loss in 2009, extended his record to 62-1 on the Paris clay having not dropped a set at this year's event.
The Spaniard made only five unforced errors in the first two sets - 10 in total - even though he was broken in the second as world No.65 Mayer showed his claycourt skills.
Nadal ended the contest with a service winner to set up a meeting with unheralded Serbian Dujan Lajovic, who beat American Jack Sock 6-4 7-5 6-3 and also has yet to drop a set.
(Reporting by Julien Pretot; Editing by Toby Davis)
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