The top-ranked Williams came into the season-ending tournament after injuries forced her out of her previous two tournaments and with the off-court distraction of disparaging comments about her from Russian tennis official Shamil Tarpischev.
Before the WTA Finals, Williams retired from the China Open and Wuhan Open because of illness and a left knee injury that had her in doubt for Singapore. But with the win over Ivanovic, she closed in on Martina Navratilova's record of 21 straight wins at the tournament.
"I just found out last time that I was 15 matches and I was like, 'Oh boy, not another streak,'" Williams said. "So now I'm 16 and, gosh, here we go again."
In the other Red Group match, Simona Halep beat Eugenie Bouchard 6-2, 6-3 in a meeting between the only two newcomers in the eight-player field.
On Tuesday in the White Group, Maria Sharapova will take on Caroline Wozniacki and Petra Kvitova will face Agnieszka Radwanska.
The top-ranked Williams was shaky in her opening service game, having to save two break points, but soon settled and took a 4-1 lead. Ivanovic got back on serve at 4-4 and had a crucial break opportunity to go up 5-4 but missed a volley.
"That was a huge point but it was actually quite a hard volley, the ball was dropping fast and I didn't come in fast enough," Ivanovic said. "I kind of got down a little bit on myself, then I rushed a little bit that (next) service game, so that was a little bit disappointing."
In the final game of the opening set, Ivanovic fell behind 0-40 and eventually dropped serve on a double-fault one of seven she made during the match.
Ivanovic came from a set down to beat Williams at the Australian Open, and looked capable of a similar comeback when she broke in the opening game of the second set, but the American immediately broke back.