Austria's Tagger, who is 28 years younger than the former world number one, eased through 6-2, 6-2 in southern China.
Williams, a seven-time Grand Slam singles champion, last won a singles match on the WTA Tour in July last year.
Now ranked 599 in the world, Williams last played at the US Open in August-September, when she lost in the first round in straight sets to Sofia Kenin.
Williams won in the doubles with Indonesia's Janice Tjen in Guangzhou on Monday.
They will play again on Wednesday.
The 53rd-ranked Tagger faces Magda Linette of Poland in the next round.