"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.
Viviani's victory was the flawless 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.
"A Tour stage was the only win I was missing, now I've got it", Viviani said happily. "It was a big goal of the year", said Viviani, who dedicated his win to his fiancée and parents.
Team EF Education First rider Michael Woods of Ottawa was 64th in the stage, but moved up one spot to 10th over all.
"I only had to finish it off in the last 180 metres".
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.
"What a attractive way to start the tour here in France", he said.
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She was served wine in his kitchen, given $300 when she left and was frequently invited back by his secretary. Vance's office did not respond to request for comment at the time of publication.
The Deceuninck-Quick Step rider took a huge gamble with his long range effort.
The difference on the day was made by Viviani, who had the speed and strength to hold off the hard-charging Kristoff and Ewan.
"I heard people say my name every 10 seconds, it's a day I will never forget", world number one Alaphilippe, who previous year won the mountains classification and claimed two stage wins, told reporters.
Defending champion Geraint Thomas of Great Britain remains in seventh spot.
"I enjoyed every kilometre today and at the end we got a attractive victory so it was incredible", Alaphilippe said. "I was just looking in front, making sure I stayed upright", said Thomas, who had a scare on stage 1 when he flew over barriers but avoided injury.
Under bright sunshine in Reims, three riders attacked from the off.
A three-man breakaway featuring Frenchman Yoann Offredo, Swiss Michael Schaer and Belgian Frederik Backaert was kept on a tight leash by the peloton and they were all reined in 16 kilometres from the finish as Deceuninck-Quick Step worked to set up Viviani's victorious sprint.
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.