The Etixx Quick-Step rider looked set to take the win at the end of a 177km stage featuring 3,000m of climbing but Team Sky's Italian Viviani edged it by the slenderest of margins.
Germany's Andre Greipel, who won four stages at this year's Tour de France, was third.
Former Tour de France winner Bradley Wiggins, riding for his Team Wiggins, finished in the main bunch.
The eight-stage race finishes in London next weekend.
(Reporting by Martyn Herman; editing by Toby Davis)
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