Bora-Hansgrohe's Sagan won by a wheel length from Alexander Kristoff of UAE Team Emirates, with both overhauling French hope Arnaud Demare of Groupama-FDJ in the final few metres of the 169.5km stage from Bourg d'Oisans.
It is a third victory of the Tour for Sagan, who extends his advantage in the points classification.
Quick-Step Floors' Philippe Gilbert tried to take advantage of a slight drag up to the finish line and the decimation of the sprint field through abandonments in recent days as he attacked when they passed under the flamme rouge.
The Belgian was caught with 300 metres to go, leaving the fast men to fight it out.
Sagan won stages two and six of this Tour, and now has 11 Tour stage wins to his name.
After the drama of his back-to-back mountain stage wins in the Alps, Team Sky's Thomas was looking forward to a quieter day as the race rolled out of the hills and began the journey west towards the Pyrenees.
While there was no drama for Thomas in racing terms, there was an incident inside the final 20 kilometres when a spectator appeared to throw a lit flare into the peloton, close to head height for the passing Sky riders who were on that side of the road, though all of the riders passed safely.
Thomas crossed the line in 25th place on the day, with all the main contenders together to keep the same time gaps.
Thomas leads the race by one minute 39 seconds from team-mate Chris Froome, with Team Sunweb's Tom Dumoulin a further 11 seconds back.
LottoNL-Jumbo's Primoz Roglic is fourth, two minutes and 46 seconds down, after Bahrain-Merida's Vincenzo Nibali was forced to withdraw having crashed on Thursday's stage to Alpe d'Huez.
"I didn't actually notice it," he said. "Sixteen kilometres to go, did you say? I was fully in the zone then fighting for position. It was pretty stressful so I had no idea."
However, the Welshman did, for a third straight day, hear boos as he collected his yellow jersey.
Asked why, he said: "I think that's a question for the people out there. I don't know. We just train hard, work hard and come here to try to win the race. That's a question for the people on the side of the road."
