Roger Federer avoided an early exit at the 2018 ATP World Finals with a straight-set win over Dominic Thiem on Tuesday.

Kevin Anderson was also victorious in the earlier match at London's O2 Arena. He followed up his opening win over Thiem by thrashing Kei Nishikori in straight sets.

Here's a look at what Tuesday's results mean ahead of the final games in the group:

Tuesday's Results, Group Lleyton Hewitt

(4) Kevin Anderson bt. (7) Kei Nishikori, 6-0, 6-1

(2) Roger Federer bt. (6) Dominic Thiem, 6-2, 6-3

Wednesday's Schedule, Group Guga Kuerten

Not before 2 p.m. GMT/10 a.m. ET: (1) Novak Djokovic vs. (3) Alexander Zverev

Not before 8 p.m. GMT/3 p.m. ET: (5) Marin Cilic vs. (8) John Isner

Tuesday Recap

Federer took on Thiem knowing that a defeat would eliminate him at the group stage of the tournament.

The Swiss star started slightly better in a scrappy opening and secured an early break to move into a 2-1 lead after Thiem overhit a shot down the line.

Federer quickly consolidated his lead, with Thiem's return of serve failing to trouble his opponent. 

James Benge at the Evening Standard highlighted the difference between the two players:

A second break of serve allowed Federer to take charge of the set at 5-2. Thiem netted an overhead, double-faulted and then misjudged another volley to hand Federer the break.

Metro's George Bellshaw was critical of Thiem's volleying:

Federer clinched the first set and swiftly took another early break at the start of the second. More sloppy play from Thiem gifted the second seed a 2-0 lead.

The 37-year-old was not at his best but did not need to be against an out-of-sorts Thiem, who failed to force a single break point. 

Thiem's 34th unforced error of the match saw the Austrian send a volley wide to hand Federer another break and the match.

Meanwhile, Anderson made light work of Nishikori, who came into the match on the back of a three-set victory over Federer on Sunday.

The South African converted his third break point in Nishikori's first service game before racing away with the first set in just 32 minutes:

A below-par Nishikori had no answer to Anderson's powerful serving and aggressive returning, and he only managed to finally win a game at 5-0 down in the second set.

Anderson just missed out on becoming only the second man to claim a double bagel at the ATP Finals:

The fourth seed served out the match in the next game. He described the win as one of the best in his career after the match:

It was a tough night for Nishikori, with the result equalling his worst-ever tour defeat, matching a 6-0, 6-1 loss in 2008, per the tournament's official website.