Expectations that the US Open quarter-finals would bring together last year’s finalists were shredded on Sunday when Rafael Nadal won after a struggle and Kevin Anderson was a brave but exhausted loser in matches of stark contrast. However there will be a rerun of the French Open final, as Nadal’s opponent on Tuesday is Dominic Thiem.

The Austrian, a first-time finalist at Roland Garros this year, has been strangely out of sorts over the first week of the final slam. A change of surface will probably do the ninth seed no favours against the defending champion as Nadal has been hitting the ball with his customary venom.

Their head-to-head favours Nadal 7-3, the most recent meeting being that final in Paris, when the undisputed master of clay allowed Thiem just nine games in two hours and 42 minutes. In fact they have played all their 10 matches on clay, but Nadal has a pedigree across all the surfaces.

Thiem said later: “On clay, it’s one of the biggest challenges in sports to beat this guy or to compete with him. I hope that it’s a little bit more comfortable on hard court – but I’m not sure.”

It was difficult not to feel sorry for the wholehearted Anderson when Thiem put him to the sword for only the second time in their eight meetings, 7-5, 6-2, 7-6 (2) in two hours and 37 minutes. On the Arthur Ashe show court, the pity was reserved for Nikoloz Basilashvili, the last unseeded player on this side of the draw, who did far better against Nadal than he did in their only previous meeting (taking a single game off him at the French Open last year).

But Nadal soaked up his resistance to win 6-3, 6-3, 6-7 (6), 6-4. Nadal fashioned his first break points on the half-hour and Basilashvili cracked when he was stretched on the deuce side by a wicked, angled forehand. The first set was soon his, and all looked well for him.

When he broke and held quickly at the start of the second, echoes of missed opportunities against the stubborn and classy Russian, Karen Khachanov, in the third round began to fade. That was a match – the longest of the first week at four hours and 23 minutes – that could have derailed Nadal’s championship campaign, but he was now back to his Sunday best against Basilashvili.

Nadal was profligate at the start of the third, though, wasting five opportunities to break, then handed his dogged opponent the lead for the first time, broken on second serve by a piercing crosscourt forehand. But Nadal’s uncanny habit of breaking back quickly took the wind out of Basilashvili’s charge and they were back on level terms with the finish line getting closer.

There were a couple of anxious moments for Nadal when Basilashvili went two points up on the Spanish serve in the ninth game, but butchered a straightforward passing shot and the moment was gone. He held once to stay in the match, and again to force the tie-break, where, against expectations and looking spent, he shocked the packed stadium to take it to four sets.

He immediately fell behind and looked exhausted and doomed but found inspiration to level at 3-3. Nadal, though, struck again with a freakish forehand down the line on the run. From there to the end, Nadal regained his composure and closed it out after three hours and 18 minutes with his seventh ace.

“Two tough matches in a row,” was Nadal’s response when asked if this was harder than his long four-setter against the Russian Karen Khachanov on Friday. “I had big chances at the beginning, but he played fantastic. A lot of credit to him, hitting the ball very, very strong. I think I improved my level at the end. I did what I had to do. I found a way. Thiem is a great opponent, big serve. It will be a tough one.”

There was no such drama for Anderson. A year ago, the 6ft 8in South African lit up of this tournament as both the tallest finalist and lowest ranked in the modern era, losing in three sets to Nadal. Two months ago, Novak Djokovic stopped him in straight sets in the Wimbledon final, where he did well to even get to the line, after coming from two sets down and saving a match point against Roger Federer in the quarters, before taking six hours and 36 minutes – the second-longest match in slam history – to beat John Isner in the semis. History, it seems, visits him only to leave him just short of glory.

Anderson, a two-time slam finalist and world No 5, did not get a sniff of playing on the main court, but he would only say: “I understand the guys out on Ashe are superstars of our sport. They get a lot of people watching. I need to win a few more tournaments to get out there. I wanted to be here right till the end and put myself in contention of winning my first major. It wasn’t meant to be.”

Having come through a taxing five-setter to beat the young Canadian Denis Shapovalov on Friday, his second full-course match of the tournament, he looked as if he would be back in the locker room in under two hours when he dropped the first two sets. He managed to stretch it to a third-set tie-break, but Thiem had too much left.