The 32-year-old Spaniard, who has been struggling with a virus, prevailed 6-3, 6-3 on the Manolo Santana court at La Caja Mágica.

Nadal took the first break point of the match in the eighth game before clinching a tight first set on day four of the Association of Tennis Professionals World Tour Masters 1000 event.

Eighteen-year-old Aliassime saved five match points on his serve in the second set but five-time champion Nadal won the sixth to wrap up the win.

Awaiting the world number two in the last 16 is the United States' Frances Tiafoe, who beat Germany’s Philipp Kohlschreiber 6-4, 3-6, 6-3.

Also progressing today were third-seeded German Alexander Zverev, who defeated retiring Spaniard David Ferrer 6-4, 6-1, and sixth-seeded Japanese Kei Nishikori, who overcame Bolivia’s Hugo Dellien 7-5, 7-5.

There was disappointment, however, for seventh-seeded Argentinean Juan Martín del Potro as he fell to a 3-6, 6-2, 5-7 loss against Serbia’s Laslo Đere.

In the Women's Tennis Association Premier Mandatory event, top seed Naomi Osaka of Japan reached the quarter-finals for the first time with a 6-2, 6-3 victory over Belarus' Aliaksandra Sasnovich.

Standing between her and a place in the last four is Switzerland's Belinda Bencic, a 6-0, 6-2 victor at the expense of Ukraine's Kateryna Kozlova.

Another straight-sets winner today was third-seeded Romanian Simona Halep, thrashing Slovakia's Viktória Kužmová 6-0, 6-0 in just 45 minutes.

Halep, the 2016 and 2017 champion, will play Ashleigh Barty in the last eight after the Australian battled back to beat Kazakhstan's Yulia Putintseva 4-6, 6-1, 6-2.

"I don't think it was her [Kužmová's] best match," Halep told BBC Sport.

"Maybe she was nervous before the match a little bit.

"It's a big tournament and it's not easy to face the top players. 

"I've been in that position.

"I played my best tennis and I felt good on court."

Three-times defending champion Petra Kvitová of the Czech Republic is also through to the quarter-finals courtesy of a 6-3, 6-3 win over France's Caroline Garcia.

Next up for her is the Netherlands' Kiki Bertens, who defeated Latvia's Anastasija Sevastova 6-1, 6-2.