Verniaiev took his second World Cup title in succession with another masterful display, despite a fall on pommel horse, to post a winning score of 89.798.
Purvis had been ahead for most of the competition but Verniaiev produced a brilliant vault and parallel bars routine to nick it while Belarus' Andriy Likhovitskiy completed the podium.
"He is a brilliant gymnast and I really enjoyed fighting it out with him to the end," said Purvis.
"The crowd were amazing, showing so much support for everyone. Competing in front of a home crowd is always special and with the Commonwealth Games and 2015 World Championships to come I’m really looking forward to competing in Glasgow again in the future.
"Overall it’s been a good year for me and to end with silver from this World Cup and bronze from last weekend's World Cup in Stuttgart is a good way to finish 2013.”
Romania's Larisa Iordache won the women's title, edging out American reigning champion Elizabeth Price, with Britain's Ruby Harrold and Raer Theaker in seventh and eighth respectively.