Earlier, Nadal's 21-match winning streak on the clay court and 50-set winning streak was broken by Austria's Dominic Thiem in their last-eight clash of the Madrid Open.
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.
The Spaniard, who received a first-round bye, kicked off his campaign in Foro Italico with a comfortable 6-1, 6-0 win over Bosnian tennis star Damir Dzumhur in their round-of-32 clash that lasted exactly one hour.
"It was a positive match, of course", said Nadal, as quoted by the Express.
"I played very well today", said Thiem.
"I will do all of the exams now and then I will try to make a good decision for the future".
Maria Sharapova saved two break points in the third set to get past Dominika Cibulkova 3-6, 6-4, 6-2. Serving at 3-5 to stay in the set, Shapovalov fell behind 0-30 when Nadal hammered a return of first serve for a victor.
But the Austrian says he is optimistic about putting together a good run at Roland Garros, which starts on May 27, and where Thiem has reached the semi-finals in the past two years. The Madrid loss was clearly an aberration and Rafa is definitely looking determined to head to Paris with an eighth title on claycourts of Rome.
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The world No 2 was expected to brush the 19-year-old aside easily and immediately piled on the pressure, forcing three break point opportunities in the first game of the match.
Rounding out the day's action, 10th-seeded Spaniard Pablo Carreno Busta bested American Steve Johnson 6-4, 2-6, 6-4; Frenchman Benoit Paire upset 14th-seeded Argentine Diego Schwartzman 2-6, 6-4, 6-2 and Great Britain's Kyle Edmund defeated 16th-seeded Frenchman Lucas Pouille 6-2, 7-6 (3).
Djokovic, a four-time champion on the comeback trail three months after elbow surgery, eased past Georgia's Nikoloz Basilashvili 6-4, 6-2.
Venus Williams fell to her second defeat in a week to Estonia's Anett Kontaveit losing in the third round match in straight sets in 1hr 19min.
Dane Wozniacki was given a scare by Latvia's Anastasija Sevastova before closing out the match 6-2, 5-7, 6-3.
Halep next plays U.S. Open champion Sloane Stephens or seventh-seeded Caroline Garcia.
Kontaveit, 22, 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 in 1999. Due to that, the southpaw not only failed to defend his Madrid title but also had to relinquish the top ranking to his greatest nemesis, Roger Federer.