Defending champion Nadal committed only 10 unforced errors and broke the 27-year-old Mayer seven times as he claimed his third victory in three meetings with the Argentine in two hours and 17 minutes.
"It was a positive [first week]," said Nadal. "I have three matches that I think I played under control. That's always positive and good. Always [being in] the second week is great news, and winning in straight sets is a little bit better. I'm happy for that."
The Spaniard is bidding to win an unprecedented five successive Roland Garros crowns and improved to a 62-1 tournament record. His lone defeat on the Paris clay came in the 2009 fourth round against Robin Soderling. Since then, he has won titles in 2010 (d. Soderling), 2011 (d. Federer), 2012 (d. Djokovic) and 2013 (d. Ferrer).
Nadal leads the ATP World Tour with a 37-6 match record in 2014, taking in titles in Doha (d. Monfils), Rio de Janeiro (d. Dolgopolov) and Madrid (d. Nishikori). The left-hander came into Roland Garros on the back of a runner-up showing in Rome (l. to Djokovic).
The 27-year-old Nadal goes on to face Serbia’s Dusan Lajovic who, like Nadal, is yet to drop a set at Roland Garros. World No. 83 Lajovic reached the fourth round of a major for the first time as he beat fellow young gun Jack Sock 6-4, 7-5, 6-3 in two hours and 14 minutes.
Looking ahead to the clash with Lajovic, Nadal commented, "He's young. He's a good player. I saw him play a few times on TV. It's great to have new players on tour, young players on the tour that are coming strong. Hopefully not too strong! We'll see on Monday. I hope to be ready for that."
The 23-year-old Lajovic had won just five tour-level matches this season coming into Roland Garros and will attempt to record his first Top 10 win (0-2 record) when he faces Nadal for the first time on Monday.
"It's my first Roland Garros main draw appearance and first time in the fourth round, so I can't be more happy than this," said Lajovic. "Maybe to play Rafa on Chatrier is one of the biggest dreams and biggest challenges. So for sure it's not going to be easy.
"You need to have a lot of tips and confidence to beat [Nadal], but I hope to enjoy the match if he wins and to give my best."