Dokic has had a dismal year, slipping to 25th in the world, and, despite not finding her best form, the 20-year-old did enough to defeat American Rubin, ranked 10th in the world.
The Yugoslav, who rose to a career high ranking of fourth last year, was far from her fluent best as she made 16 double faults and 40 unforced errors but she fought bravely to get past the more fancied Rubin.
"I am low on confidence right now," said Dokic, who has suffered first-round defeats in Filderstadt, Germany, and Moscow in the past two weeks.
"It's a confidence thing for me and once I get that back things will be better. It's going to take time and I need to work towards next year."
Dokic will now face Alexandra Stevenson in the second round after the American beat Swiss wild card entry Myriam Casanova 3-6 7-5 6-3.
Spain's Conchita Martinez was another first-day casualty as she suffered defeat to American qualifier Amy Frazier.
Frazier, the world number 75 who came through three qualifying rounds in Zurich, recovered from a set down to overcome veteran Martinez 4-6 6-4 6-1.
Martinez, ranked 13th in the world, suffered a second round defeat to Justine Henin-Hardenne in Filderstadt, Germany last week and failed to discover her form as Frazier comfortably won the deciding set.
Frazier will face seventh-seeded Vera Zvonareva in the second round after the Russian overcame American Meghann Shaughnessy 6-0 4-6 7-6 in the final game of the day.
Sixth-seed Ai Sugiyama of Japan came through a tough encounter with Spanish qualifier Magui Serna 6-3 3-6 6-1.
Serna, who qualified for the main draw as a lucky loser after the withdrawal of injured American Lindsay Davenport, saved 11 break points as she pushed Sugiyama all the way.
Another qualifier, Tina Pisnik, awaits Sugiyama in the second round after the young Slovenian got past South Africa's Amanda Coetzer 6-3 6-0 in straight sets.
Israel's Anna Pistolesi won Monday's opening game 6-2 7-5 against Italy's Silvia Farina Elia and faces second seed and world number two Henin-Hardenne in the second round.
