Philippe Gilbert, Bob Jungels and Alejandro Valverde complete the top five, with defending champion Chris Froome sitting in eighth - 1 minute and 43 seconds behind van Avermaet.
Thomas, of Team Sky, completed an impressive ride on the 108.5km stage from Albertville to the summit of La Rosiere by overtaking Spaniard Mikel Nieve (Mitchelton) in the closing metres. Some guys might sit here and give some PR bull**** but I just say how it is with me and that's how it is.
The major question now may concern the dynamics between Thomas and Froome within Sky.
Despite a distinct lack of support from the French locals, Team Sky's Geraint Thomas remains in possession of the yellow jersey at this year's Tour de France.
Double-stage winners Fernando Gaviria and Dylan Groenewegen, plus Andre Greipel, were among six riders to abandon mid-stage, while Rein Taaramae crossed the line in tears as one of two to miss the time cut. I think it's great for us to have those options to be able to play when it comes down to it, especially looking at rivals that have two or three options within their teams. You never know how the body reacts and I'm still riding for Froomie, he's still the man. For me, whatever happens now it is a super successful Tour.
Primoz Roglic - the Slovenian is quietly going about his business after stellar form this season saw him win key lead-up races Pais Vasco and Romandie.
Dumoulin, the time trial world champion, is Sky's closest challenger.
Thomas takes stage win and yellow jersey on Tour de France
Implementing cobble sections into a stage is a step too far for future Tours, with only 50 per cent of the riders having little to no experience in navigating these risky conditions.
In 2013, French freeride mountain biker Romain Marandet jumped over a group including eventual victor Chris Froome of Team Sky during the 100th edition of the race.
Thomas could feasibly be in yellow by Tuesday evening as stage 10 takes the peloton over four categorised climbs in 158.5km of racing between Annecy and Le Grand-Bornand, territory which does not suit Van Avermaet.
Sky calmly rode at its own pace and slowly caught a series of breakaway riders before Thomas kicked into action with 6 kilometers remaining.
"I didn't plan to go in the breakaway, but once I did, I just had to go for it". Jakob Fuglsang of Astana was next at 3:12. Thomas has the yellow jersey and "we respect him for that", Bernal said of the two-time Olympic track cycling gold medalist.
But when it comes to targeting a fifth yellow jersey - and what would be his fourth Grand Tour win on the trot after winning the Tour of Spain and the Giro d'Italia in the wake of his 2017 yellow jersey triumph - Froome is on easy street. "To do it two years in a row is really nice".