Taurasi scored 16 points in the first quarter, sinking 4-of-5 from 3-point range as the Americans took a 31-21 lead and rolled to a Group B preliminary round win.
Breanna Stewart scored 17 points and Tina Charles added 15 points and eight rebounds for the US women, who matched Group A leader Australia with the best Rio record at 3-0.
Canada can go 3-0 with a victory over winless Senegal in a later Group B contest.
Danielle Page, Jelena Milovanovic and Sonja Petrovic each scored 15 points to lead Serbia.
US women have won seven of the past eight Olympic crowns and last lost an Olympic contest in the 1992 Barcelona semi-finals.
In other games, Alba Torrens scored 32 points and Astou Ndour added 21 to power Spain over China 89-68. Ting Shao led China with 14 points.