It doesn’t do to prod the sleeping lion. Roger Federer, who played as if he had been tranquillised in a desultory opening defeat by Kei Nishikori, swept away the limp challenge of Dominic Thiem in little over an hour on Tuesday night, and looks in the mood to prove a few people wrong in the 2018 ATP World Tour Finals.

However, allegations this week by the semi-retired French player Julien Benneteau that Federer has often received preferential treatment over scheduling, and had undermined the integrity of the Davis Cup with his company’s promotion of the exhibition Laver Cup, met with a cool reception afterwards.

“Julien, who is a nice guy, I know him since the junior times,” Federer said after an impressive 6-2, 6-3 win that hauls him back into contention for the semi-finals. “But I think all of this has been totally taken out of context. I don’t really feel in the mood during a World Tour Finals to discuss that topic, to be honest. I get asked, ‘Would you like to play Monday or Tuesday’ sometimes. Sometimes I get asked, ‘Do you want to play day or night?’ Sometimes I get help, sometimes I don’t.”

Victory over a bedazzled Thiem, meanwhile, saved the six-times champion from the more immediate embarrassment of expulsion from the final big tournament of the season, although he probably still needs to beat a rampant Kevin Anderson on Thursday to get out of the round-robin stage for the 15th time in 16 visits. He will not lack for motivation. “It’s never easy to play against him, whatever the surface, as he showed against me at Wimbledon,” Federer said of Anderson, who beat him in five gruelling sets in the quarter-finals this year.

It was a pointedly different scenario against Thiem. After half an hour Federer had secured the first set and the Austrian, who has had a good season, lost all shape and confidence. This was not the Federer who played so distractedly on Sunday night, before leaving the venue with unseemly haste. On Tuesday night, he was making a statement, to the rest of the field and, perhaps, to Benneteau.

The Swiss broke for the third time to wrap it up in 65 minutes – one more than it took Anderson to beat Nishikori for the loss of a single game earlier in the day.

While at times Federer has looked to be playing from memory in the latter part of the year, his pedigree shone through on one of his favourite stages. Admittedly, it is some memory. He is still No 3 in the world, has won four titles this year, lost only 10 of 57 matches and earned more than $7m. He is not exactly on the scrapheap.

Nevertheless, as Annabel Croft noted on Sky, there were signs of the tennis “yips” in his straight-sets loss to Nishikori, and the Swiss gave the impression he was out of sorts during the match and afterwards.

“I don’t think I beat the best Roger,” the impossibly polite Nishikori reflected on Tuesday, after his own devastating collapse against Anderson. The 32-year-old South African – alongside his former college rival, John Isner, 33, the oldest debutants in the event since 1972 – rated his blindingly quick match as “among the best I’ve played”, adding “I kept at it the whole time”. There was little argument from the loser, who could only say later: “It wasn’t my day. I played one of my worst matches this year.”

Anderson, powering down his serve from on high, full throttle, aced Nishikori 10 times and converted five of 12 break chances. It was almost an unfair fight. AndersonThe South African, who has resurrected his career in a dogged fightback from hip surgery to stand alongside the best in the world over the past 18 months, knows he has an excellent chance of breaking through here, after reaching the final of the US Open in 2017 and Wimbledon this year.

For years, he toiled on the fringes of the elite. He was always dangerous but only rarely disturbed the natural order. Now, as weariness hangs over his peers, he has a chance again. If he were to win, it would be celebrated in all corners of the game.

In the first evening match, Jamie Murray and his long-time Brazilian partner Bruno Soares sealed their advance to the semi-finals and looked sharp in beating the second-seeded Colombians, Juan Sebastián Cabal and Robert Farah 6-4, 6-3 in an hour-and-a-quarter.

It was a deal easier than their first-round win over the sixth seeds, South African Raven Klaasen and New Zealander Michael Venus, and they can now play with some freedom in the redundant third match against Nikola Mektic and Alexander Peya, who lost in straight sets on Tuesday to Klaasen and Venus, although they did take them to two tie-breaks.