Froome, who won the Tour in 2013, 2015, 2016 and 2017, was cleared of a doping offence just before the start of the race after he tested positive for excessive levels of an anti-asthmatic drug during last year's Vuelta.
Froome is team leader at Sky, owns 6 Grand Tour titles and can win a record-equalling 5th yellow jersey here.
The GC group were well behind but some late fireworks saw Primoz Roglic (LottoNL-Jumbo) grab a few seconds while the top three overall - Geraint Thomas and Chris Froome (Team Sky) and Tom Dumoulin (Team Sunweb) finished together to put time into their other rivals.
Team-mate Chris Froome came in third, alongside Dumoulin, some 20 seconds later in a pretty much flawless day for Team Sky as they made up time on their rivals. From there, he sprinted to his stage victory at the airport of Mende, just in front of Julian Alaphilippe and Jasper Stuyven.
Sagan's 11th career win at the world's biggest bike race came after he was the fastest to the line in bunch sprints on Stages 2 and 5.
Facing no attacks on the flat stage, Thomas had no trouble maintaining his advantage of 1 minute, 39 seconds over defending champion Froome.
On Thursday, Froome was on stage 12 when a random guy from the crowd made a decision to run up to him and push him as he was racing.
"(Dumoulin) can really pace himself", Thomas said. I knew it would be hard, especially because the group was really big. Froome initially held back, marking counter-moves from AG2R La Mondiale's Romain Bardet and UAE Team Emirates' Dan Martin before leaving them both behind and catching Dumoulin.
With the Tour dropping down from the Alps, there were only two categorized climbs for the riders to contend. De Gendt won the first of the day at Côte de Brié while Scully won the second at Côte de Sainte-Eulalie-en-Royans.
Stage 15 on Sunday from Millau to Carcassonne is another hilly leg before the race's second rest day on Monday.
Saturday's Stage 14 is a hilly 188-kilometer trek from Saint-Paul-Trois-Chateaux to Mende as the race makes its way to the Pyrenees Mountains. "It's not an easy stage", said Froome. When Froome accelerated, I followed him, and I felt good, too, but then there was this slowing down, and I went down.
Welshman Thomas has no reference on a three-week race and he has been insisting he could "lose 10 minutes" on a bad day in the mountains, but his recent form suggests he can keep the yellow jersey all the way to Paris.
- Trump ready to hit all Chinese imports with tariffs
- ‘I was confident German Grand Prix win would stand,’ says Lewis Hamilton
- Francesco Molinari wins the British Open
- Authorities say 1 killed in LA market standoff
- 9 of 17 Dead in Missouri Duck Boat Accident From Same Family
- Melania Trump's Face During Meeting With Vladimir Putin Goes Viral
- Syria rebels 'agree deal' to surrender Quneitra
- Trump and Putin 'discussed Ukraine' crisis at Helsinki summit - Russian leader reveals
- OKC trades Melo to Hawks for Dennis Schroder
- Trump backtracks on Helsinki comments - PM