However, Shapovalov recovered to hold and saved five more break points in his next service game to keep the set on serve. Unfortunately for the Italian, he has lost their five meetings since that win, although he did manage to take a set off Nadal in Madrid a year ago.
"I think Rafa played incredible today", said Shapovalov.
Sixth seed Thiem crashed out just a week after inflicting a first clay-court defeat on Nadal in over a year in Madrid which cost the Spaniard the world number one ranking. And I was a little bit more relaxed, and I was able to not have more mistake with it, too.' About his quarter-final against Fabio Fognini, Nadal said: 'I'm going to prepare like every day. Fifth seed Juan Martin del Potro emerged a 7-5, 6-3 victor over Barcelona runner-up Stefanos Tsitsipas and Miami Open champion John Isner was edged 7-6 (5), 6-7 (2), 6-7 (5) by Albert Ramos-Vinolas.
Nadal will next face Canada's Denis Shapovalov, who faced a grueling test in battling past Dutchman Robin Haase 7-6 (3), 6-7 (5), 6-3 in almost two and a half hours.
The 24-year-old destroyed his racket in fury as he suffered his first defeat to Italian Fabio Fognini in three meetings, sinking 6-4, 1-6, 6-3 at the Foro Italico.
In other seeded action, second-seeded German Alexander Zverev bested Italian wild card Matteo Berrettini 7-5, 6-2.
"I played really a good tactic, making him run a lot from both side", said Goffin.
Also, U.S. Open champion Sloane Stephens held off a comeback from Estonian qualifier Kaia Kanepi in a 6-0, 5-7, 6-4 victory; seventh-seeded Caroline Garcia defeated Timea Babos 6-3, 6-4; and 14th-seeded Daria Kasatkina eliminated American qualifier Danielle Collins 6-2, 6-3.
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The Czech went on to lose that game and the match 3-6, 6-3, 7-5 in two hours 21 minutes.
The Romanian, a finalist in Rome previous year, is on her way to holding her top ranking as she next plays France's Caroline Garcia or American Sloane Stephens.
Halep needs to reach at least the quarterfinals or risk losing the top spot to Caroline Wozniacki.
Wozniacki faces 15th-seeded Anastasija Sevastova in a late match.
Fourth seed Marin Cilic displayed plenty of patience during his 6-3 6-4 win over Frenchman Benoit Paire.
Three-time victor Maria Sharapova ousted Daria Gavrilova 6-3, 6-4 and will play fifth seed and French Open champion Jelena Ostapenko who saw off Britain's Johanna Konta 2-6, 6-3, 6-4.
The 22-year-old Kontaveit won through 6-2, 7-6 (7/3) against the 37-year-old American who was seeded eighth in a tournament she won almost two decades ago to 1999.