Roger Federer recovered from his first-match nightmare to keep alive his hopes at the ATP Finals with a comfortable victory over Dominic Thiem.
Switzerland's Federer, knowing defeat would mean he would not advance from his group, beat the Austrian 6-2 6-3.
The six-time champion had slumped to a shock defeat by Kei Nishikori on Sunday but he cut down on his errors to win.
Next up for Federer on Thursday is Kevin Anderson, who beat Nishikori 6-0 6-1 earlier in the day.
The action in London continues in the other group on Wednesday, when world number one Novak Djokovic plays Alexander Zverev.
Just before walking on to the court, Federer spoke of the need to be "more positive" in his mindset.
He arrived with a little smile and a few waves before making his intentions clear from the very first game where he carved out a break point.
Although he failed to convert that one, he made no mistake in Thiem's next service game and celebrated with a fist pump when the Austrian sent a forehand long.
This was a completely different Federer to the one who had looked frustrated and grouchy against Nishikori in his opening round-robin match on Sunday.
And it was not just his mood that had improved considerably; his statistics had too.
Gone were the 34 unforced errors - instead a much more disciplined 11 - and with that a superb rate of 86% of first-serve points won and 81% of second-serve points.
He looked more like his old self and was helped by Thiem's errors, summed up when the Swiss sealed victory after the world number eight hit a forehand long.
"It feels good. I am very happy that I showed a reaction after the last match," Federer told Sky Sports.
"Today I was more positive and happy on the court. I love playing in London and I had to remind myself what a privilege it is. I hope I showed it."