Fitton, twice a Lakeside semi-finalist, missed six match darts before Harbour hit double six to reach the last 16.
Three-time runner-up Tony O'Shea is also out, beaten 3-0 by Welsh 12th seed Jim Williams in the tournament's opening match.
It is the third year running that unseeded O'Shea has lost in round one.
Craig Caldwell of New Zealand will play the defending men's champion, England's Scott Mitchell, in round one on Sunday after the Kiwi thrower beat Scotland's Alan Soutar 3-1 in a preliminary-round match.
Middlesbrough's Glen Durrant, the number one seed, faces Welshman Dean Reynolds in the final game of Saturday's evening session.
In the women's draw, reigning women's champion Lisa Ashton made it safely through to the last eight.
The 45-year-old from Bolton dropped just one leg in her 2-0 win over England's Paula Jacklin as she began her quest for a third consecutive women's world title.
Media playback is not supported on this device
Seventh seed Darryl Fitton is out of the BDO World Championships, losing his first-round tie to fellow Englishman Dennis Harbour in a sudden-death leg.