South Korea's Lee Eun-byul took the silver and compatriot Park Seung-hi picked up the bronze in a race featuring eight skaters instead of six because of advancements.
The final was thrown wide open after Wang was disqualified in the semi-finals for impeding in a crash near the end of the race.
Wang, the 2006 bronze medallist, had been seeking a second gold of these Games after winning the 500 metres earlier this week.
"When I saw she fell, I thought 'oh no' and when I heard she had been disqualified, my heartbeat went faint again and I thought 'oh no' again," said the 18-year-old Zhou, whose own semi-final was due to take place just moments later.
"At that point I was affected and I really didn't know what I was going to do to continue my race. I don't think I did a very good job in the semi-finals as my mood was affected."
Zhou's bad mood did not last too long and the 2009 world silver medallist waited for the right moment in the final to rip through the field and take a commanding lead over the line.
She did not wait for the official result to confirm she had won, draping herself in a Chinese flag for a victory lap.
"This was the gold I wanted but there is another gold I want so stay tuned," she mysteriously told reporters.
Her victory meant China had won both the women's finals contested in Vancouver.
American Katherine Reutter, widely tipped for the podium, destroyed her chances when she bumped into Park with six laps to go in the final, possibly costing the South Korean a better medal as she also lost speed after the impact and had been leading at the time.
"This was my race and it didn't happen," Reutter, her face reddened from crying, said after finishing fourth.
"I'm upset at myself, I made a mistake and I messed up. I tried to pull an inside pass and it didn't happen. I messed up some people around me and I'm very sorry for that."
Britain's Elise Christie refused to make any excuses after crashing out in the heats.
The 18-year old, who won silver at the recent European Championships in Dresden, admitted the big-stage nerves got to her.
She had shown encouraging form over 500m and was looking forward to competing over her preferred longer distance.
But she failed to get past Bulgaria's Evgenia Radanova - who she has consistently beaten all season - to secure a place in the top three.
"It certainly didn't go as expected. I was really nervous and I just messed it up," said Christie.
"I think I let the whole experienced get the better of me and I need to move on, learn from this and get on with it."
Place of birth: Changchun, China
Residence: Beijing, China
No previous Olympic results
Gold, 2009 World Championships, 3000m relay
Runner-up, 2008 World Championships, overall
Silver, 2009 World Championships, 1500m
Silver, 2008 World Championships, 1000m
Silver, 2007 World Championships, 3000m relay
Third, 2009 World Championships, overall
2x Bronze, 2008 World Championships, 1500m, 3000m relay
Bronze, 2007 World Championships, 1000m
2x Champion, 2009/10, 2008/09 World Cup, 1500m
Background: Zhou started skating at age eight after a speed skating coach noticed her potential.