The 14-time major victor withdrew from his favourite grand slam previous year due to a wrist injury ahead of his third-round match, but looks in great shape in his quest to make history 12 months later.
Djokovic goes on to face Argentine Diego Schwartzman and Nadal takes on Nikoloz Basilashvili of Georgia.
"It's true that if it is sunny, between 18 and 25 degrees, normally it is good for me, because the ball flies and we have good bounces on my forehand, especially", Nadal added.
After dropping the opening set against Kontaveit, Muguruza was down a break in the second before coming back.
Venus Williams shook off a slow start to ease into the third round with a 6-3, 6-1 victory over Japan's Kurumi Nara.
But the fourth seed recovered to claw out a 6-7 (4/7), 6-4, 6-2 win and book a third-round clash with Yulia Putintseva of Kazakhstan. "And as I say before, I feel always excited to do what I do and to have the chance at nearly 31 years old to still be all around the world playing the tour". Now Nadal has turned for his support and ideas from another Mallorcan, fellow French Open champion, fellow former No1, Carlos Moya.
Tunisian Ons Jabeur became the first Arab woman to reach the third round at a grand slam with an upset win over sixth seed Dominika Cibulkova 6-4 6-3.
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American Steve Johnson advanced to the third round on Wednesday by beating Borna Coric 6-2, 7-6 (8), 3-6, 7-6 (6).
As we mentioned before for the first time in several years, we can't detect any massive favorite and like never in the previous 6 or 7 contests here, the competition is exciting regarding the final victor.
Those contenders have now had two quick wins each, the flawless start to any big tournament.
"I was surprised how I played even though I lost", she said.
11th seed Grigor Dimitrov picked up a comprehensive 6-3 6-4 7-5 win over Spaniard Tommy Robredo, a five-time Roland Garros quarter-finalist.
Jo-Wilfred Tsonga's hopes, however, vanished into thin air when he was sent packing with a 7-5 6-4 6-7 6-4 loss to Argentina's Renzo Olivo.
Mattek-Sands, who is back in the third round for the first time since 2013, will next face Samantha Stosur. "So it was really late", Olivo said. It was hard not to think about the restart. So a lot of things that I achieved are because he was there since I was three years old helping.
If they do meet to decide who is strongest on the opposite side of the draw to Andy Murray, who plays Martin Klizan on Thursday, it looks likely they will leave a trail of bruised spirits behind them.