The 27-year-old was taken to a deciding sprint by Australia's Stephanie Morton, the fastest qualifier in the heats, but once again the Olympic champion showed her quality when the pressure was on.
"At the moment and on this day I'm not counting," Vogel, who sat on the track draped in a German flag after her victory, said of matching Meares. "It was very hard at the end and it took me three final heats to get the gold medal.
"Today it took everything to make it to the finish line. I'm just proud to make this world title."
There were more home celebrations as Kirsten Wild claimed her second gold medal of the week to make it three wins for the Dutch so far.
Wild, who delivered Dutch gold on the opening day of the event when she topped the podium in the scratch race, won the last sprint of the points race in the multi-discipline omnium to secure the title in style, delighting the home crowd.
It was an eighth world championships medal for the 35-year-old but first gold in the omnium, having won silver last year.
Amalie Dideriksen of Denmark was second with Rushlee Buchanan of New Zealand third.
Earlier in the day Australia's Cameron Meyer controlled the men's points race to win his fifth world title in the event and ninth rainbow jersey in total.
"It's special," Meyer, who won five intermediate sprints and took two laps on the field, said. "Every one of them is special when you win a gold medal in the world championships.
"To win today was not easy. To be one of the favourites every time is a lot of pressure, but I enjoy it."
Jan Willem van Schip won silver, adding another medal to the hosts' total, with Britain's Mark Stewart third.
Italy's Filippo Ganna won the men's individual pursuit, storming back to beat Portugal's Ivo Oliveira in a nailbiter.
(Reporting by Martyn Herman; Editing by Toby Davis)
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