Rafael Nadal beat Pablo Carreño Busta in three sets of gathering power on Friday night to reach the semi-finals of the Paris Masters, and simultaneously shoehorned Diego Schwartzman into the upcoming ATP World Tour Finals in London. The Spaniard beat his compatriot 4-6, 7-5, 6-1, a few hours after the Argentinian collapsed in the first quarter-final in just over an hour against the mercurial Russian, Daniil Medvedev. Nadal has to get past Alexander Zverev on Saturday, while the other semi-final brings together Medvedev and Milos Raonic, who was impressive beating Ugo Humbert, 6-3, 3-6, 7-6 (7). Stan Wawrinka, the oldest player in the draw at 35 who came from a set down in his previous two matches, found 23-year-old Zverev too lively after a tough week. The world No 7 – distracted for days by allegations of abuse, which he denies, by an ex-girlfriend – remained focused long enough to win 6-3, 7-6 (1), in an hour and a half. Although embarrassed by his own performance earlier in the day, Schwartzman was relieved to see Nadal win, as Carreño Busta was his only rival for the eighth and final spot at the O2 Arena. The 18,000-seater opens its doors to the best eight players in the world – and very few others – on 15 November in the farewell edition of the tournament after 12 years in the capital before it moves to Turin for five years. Novak Djokovic, who was officially declared end-of-year world No 1 for the sixth time on Friday, returns in London, along with Nadal, Medvedev, Schwartzman, Zverev, Andrey Rublev, Dominic Thiem and defending champion Stefanos Tsitsipas. For all his humility, Nadal does not suffer much from self-doubt, but he must wonder in moments of introspection if, at 34, he will ever win this indoor hard court tournament. In seven attempts, the nearest he has got was his first visit in 2007, when David Nalbandian allowed him just four games in the final. “I think matches like yesterday and today help,” he said. “Semi-final here is a positive result for me. It’s been a long time since I played indoor hard.” At 29, Carreño Busta is still striving for consistency at the highest level, but his racket did not quiver when he threaded a spectacular forehand crosscourt past Nadal to win a set off his compatriot for only the second time in seven encounters. It took Nadal an hour and 17 minutes to get his first break point, which his friend and rival saved with his third ace. But, from that point on, Nadal steadily broke him down, levelling at 7-5 then, with heightened urgency, breaking to love in the fourth game of the decider. Medvedev, oscillating up and down the top 10 this season, was back to his best in beating Schwartzman, 6-3, 6-1. “He didn’t show his best tennis,” Medvedev said. “It was good to win in such a short time, good preparation for London.” Schwartzman, who broke into the top 10 for the first time a month ago after several impressive wins after the Tour resumed, was totally out of sorts. “I know that I did many things really bad, no defence, really horrible,” he admitted. The second quarter-final was going the way of the first as Raonic’s big game threatened to overwhelm Humbert, but the young French left-hander found a rhythm to level at a set apiece. Humbert held his nerve to force the deciding tie-break, and Raonic saved match point in a 30-shot rally worth a standing ovation. It might have been the best point of the week. Raonic dumped a simple return on his own match point but, after two hours and 18 minutes of an enthralling contest, Humbert’s statement sequence of eight wins in a row was over. Raonic, who has wandered in and out of the tennis wilderness, could not have finished on a more uplifting note. “I wanted to make sure I didn’t leave the court without giving it my all,” he said of his fightback in the shootout. “I was creeping towards the edge there.”