Singapore: Serena Williams jokes that she is not planning to write a sequel to her 2010 autobiography so much as a series, considering how much has occurred in the life and career of the 18-time grand slam champion. Still, at just-below-major level, Williams has also won four year-end WTA Championships, and successfully wrote the first chapter in the bid for No.5 with Monday's 6-4, 6-4 round-robin defeat of Ana Ivanovic.

Opening the eight-player WTA Finals at the 10,000-seat Singapore Indoor Stadium, Williams resumed from the break required to treat the left knee problem that she had feared would prevent her from headlining the event, and thus attempting to defend the championship that the world No.1 has won in Istanbul for the past two years.

Result: different venue; same winning start. Williams said she was not entirely untroubled by the injury that forced her withdrawal from the recent China Open, but the great American also did what she needed to against a rejuvenated Ivanovic, the former French Open champion who won four titles in 2014 and is set to finish in the top 10 for the first time since her major-winning year, 2008.

"I felt pretty good," said Williams, 33, who stretched to 16 her consecutive run of wins at the prestigious tournament, accumulated over 2009, 2012 and 2013. "I really felt like I don't really have anything to lose at this point. I just started practising on Monday, so I feel like I just got to do what I got to do and do the best that I can.

"I felt the knee a little bit, but compared to what it was in Beijing, it feels so much better. I'm getting better, which is great. Just have to keep doing my program so by the end of the week, hopefully – if I'm here – I'll still be getting better."

Ivanovic was responsible for Williams' shock fourth-round exit at this year's Australian Open, but the seventh seed is now 1-8 against the world No.1. The Serb recovered from 1-4 down to level at 4-4 in the first set, before fluffing a routine volley for a 5-4 break.

"I'm definitely very disappointed that both sets I made a few easy errors in the last service game," Ivanovic said. "Especially in the first set, you know. I had a break point in 4-all, which I didn't take and kind of got down a little bit on myself. Then I rushed a little bit in the next service game, so that was a little bit disappointing. I felt I created lots of chances, especially off the ground."

The other undefeated player from the strong red group after the opening night of competition was fourth seed Simona Halep, who dismissed Wimbledon finalist Eugenie Bouchard 6-3, 6-2.

"I played really well and am really happy to have found my game again," Halep said. "I played aggressive at the right times and hit some winners. She is a great player and is very young and will definitely be at the top for a long time."

The junior player in the field at 20, but also the most consistent grand slam player of the season with three semi-finals, Bouchard admitted she did not feel match-sharp. "But I feel like I can build on this. I still have another match, even though I lost, so there is a positive.

"That's another interesting part about this tournament. First match playing No.4 in the world. It's not like you can ease into a tournament or anything like that. You've got to hit the ground running. But it's kind of a great experience to get so many kind of high‑quality matches back to back like this.

"I feel like it's a match that I can build on, kind of get some rust off today, and just try to be a bit better in the next match."