“It's unbelievable. I can't believe this has just happened to me”
But Olympic champion Jason Kenny went out in the men's sprint quarter-finals.
Kenny was beaten 2-0 by former junior world sprint champion Sam Webster, who edged the first race after flying off the final bend in Minsk.
Their second meeting was nowhere near as close, with the 22-year-old New Zealander opening up a huge gap on the last lap that the Bolton rider could not make up.
Fellow British sprinters Matt Crampton and Philip Hindes were eliminated earlier in the competition, so Britain will have no representatives when the event concludes on the final day of these championships on Sunday.
There was to be a much happier ending for James, however. A legend like Pendleton is a tough act to follow but the Welsh rider has stepped out of her shadow after coming to Belarus in the form of her life, and will go for gold again in the keirin on the final day.
If she was a nation, James would already be sixth on the medal table, but she has helped Britain stay clear of perennial rivals Australia at the top with a total of seven medals, four of them gold.
She had demonstrated her belief and ability with third places in the
500m time trial,
as well as the manner of her faultless progress through the individual sprint rounds to reach the final.
James had been faster than Vogel all week but the German has more experience of the cat-and-mouse contests at this level, making it a fascinating match-up.
Victoria PendletonOlympic cycling champion and BBC Sport summariser
"It was a fantastic competition for Becky. She rode that third race confidently - she was clearly the winner in my eyes before the race was over. I think a lot more titles will be going her way. I'm sure she'll have a bit of a break now, though I doubt she'll want to. Then it depends on how many World Cups she wants to do next year before focusing on the World Championships again."
In the first race, James tried to lead it out to the line but her rival timed her attack perfectly and just nudged ahead at the finish.
That left the Welsh rider needing to win the next race to force a decider, and she left herself a lot to do after Vogel escaped on the back straight but had enough in the tank to reel her in and get past.
There was more tension to come in the decider. Neither rider wanted to lead out but James attacked with a lap and a half to go and held on for victory.
She celebrated it with her grandparents, who had made the long trip to Belarus - a journey that certainly seems worthwhile.
"It's unbelievable. I can't believe this has just happened to me," a jubilant James told BBC Sport afterwards. "I'm world champion and I can't believe it!
"I didn't know if I'd run the first run quite right. We went over the tactics right after. I really wanted to win this so I sat down, kept myself calm and thought about what I wanted to do in the next round, did it, and did it again in the third.
Trott triumphs in elimination race
"I didn't think I'd get a single medal - I was hoping to get top eight in everything. I can't believe I got a rainbow jersey."
Her boyfriend, Wales wing George North, was in Rome playing in a Six Nations win over Italy but he Tweeted afterwards: "Great result for the boys tonight. And my beautiful girl @BecksJames is a WORLD CHAMPION!! Well done Becks."
James is not the only British rider eyeing the podium on the final day. In the women's omnium, defending champion Laura Trott lies in the bronze medal position half-way through the six-discipline event.
Trott, who is also Olympic champion, staged a repeat of her victory over Sarah Hammer in the eliminator at London 2012 with an exhilarating ride that moved her into third place, five points off the American and three behind Poland's Katarzyna Pawlowska.
Elsewhere, Dani King finished eighth in the women's 25km points race and Jon Dibben also ended up eighth overall in the six-event omnium in his first senior world championships.
The 19-year-old, who like King is from Southampton, started the day in 11th place at the halfway mark but moved up the standings after taking fifth in the individual pursuit and winning the 15km scratch race, before signing off with 12th spot in the 1km time trial.
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