"Viviani edged out UAE Team Emirates" Alexander Kristoff and Lotto-Soudal's Caleb Ewan at the line, with Bora-Hansgrohe's Peter Sagan in fourth.
The 213.5-kilometer (133-mile) flat route from Reims to Nancy did not pose any major difficulty and was a flawless opportunity for sprinters to get a stage win.
Viviani's victory was the ideal follow-up to Julian Alaphilippe's win on Monday for the Belgian team, who retained the yellow jersey after the Frenchman was cheered on all the way from Reims by massive crowds of locals and tourists. "I won in the Giro and the Vuelta and now in the Tour de France, that means a lot to me".
"I had a Giro win and one in the Vuelta, so this was the big goal of the season".
"I had missed my lead-out in the first stage, it was my fault and I was very disappointed". "I was in a good position and I was helping my teammate but I was also scared [of crashes] because the finish was nervous".
The Italian speedster might soon be racing without his favourite teammates, however, amid reports he might join Cofidis next season as the French outfit seeks to replace its top sprinter.
Viviani was ideally set up by the Deceuninck-Quick Step leadout train in the finale and made the most of the slight uphill finish in the eastern city of Nancy.
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"No one wins the Tour on five-second sprint finishes but obviously it would be better not to have lost that", Thomas said.
With Viviani sitting in the wheel of the experienced Morkov and Richeze, Kristoff made his move and opened up with an early surge to the line.
"I've got the green jersey but I haven't got a stage win yet, I'll play it day by day - it's a long way to Paris", said the Slovak star after pulling on the green jersey again.
"I said today "I will only focus on Max Richeze's wheel", I know Morkov does an awesome job, he is the best in choosing the time and he did it perfectly today".
"Geraint is not a screamer and shouter but he knows what he wants; he's a strong character", Brailsford said of the defending champion. The breakaway riders swapped turns efficiently until Wellens attacked with 48km to go before the climb of Nanteuil-la-Forêt.
The trio was eventually caught with 17 km left, in the small Côte de Maron climb, leaving the spotlight on the fastest men of the peloton.