Van Avermaet began the day with a 43-second advantage over Thomas but most expected the Classics specialist to be overhauled by the general classification contenders as the race hit the Alps.
Instead Van Avermaet honoured the yellow jersey with a superb ride on the 158.5km stage 10 from Annecy to Le Grand-Bornand, getting into a breakaway and staying clear to the finish.
The BMC rider finished fourth as Quick-Step Floors’ Julian Alaphilippe took his first career Tour stage win, but crucially was one minute 39 seconds ahead of the main group of contenders, including Thomas and his Sky team-mate Chris Froome.
That saw the Belgian extend his overall lead to two minutes and 22 seconds over Thomas, with Movistar’s Alejandro Valverde up to third, three minutes and 10 seconds back.
If it surprised most, it did at least follow a pattern as Van Avermaet used attack as the best form of defence when spending three days in yellow in 2016 – and Thomas was not among those caught out.
“We were expecting that,” said the Welshman, who had been just three seconds off yellow for much of last week. “He did it the last time he had the jersey. It would have been nice to take (yellow) but it’s the Tour de France. Nothing comes easy.”
On Monday’s rest day, 2012 Tour winner Sir Bradley Wiggins had suggested his old team would “have a real problem on their hands” if Thomas took yellow ahead of Froome - who is 59 seconds back on his team-mate in sixth place.
Wiggins also claimed team principal Sir Dave Brailsford could be “divisive” and “self-serving” in such situations - comments Brailsford laughed off after the stage.
“I’ve been called a lot worse - on my Richter scale, that’s not bad,” he said. “I can take that. Over the years, we’ve always tried to build teams where the top guys are very close together and they have got their own ambitions.
“As you get older and wiser, and you learn from your mistakes, you know how to manage these situations, and openness is the key…
“It’s a totally different dynamic from the past – Chris and Geraint have grown up together, they have known each other a long time, they are 32 and 33 years old, they’re not young lads and they are pretty easy to manage, to be honest.”
Froome had dramas of his own on the day when he suffered a puncture on the gravel section at the top of the Montee du plateau des Glieres.
“It little bit wacky races going on there,” the four-time Tour winner said. “I had a puncture on the first section, got a spare wheel from a team-mate only to find out that was flat as well. So it was a little bit of a comedy of errors going on there.”
Alaphilippe, 26, took victory after moving off the front of the break at the summit of the Col de Romme, 28.5km from home.
He gradually pulled away as he turned a bid for the climbers’ polka-dot jersey into a first French stage win of this Tour.
The rider leading at the end of the first mountain stage has gone on to win the Tour every year since 2012 but Van Avermaet knows he will bring that sequence to an end.
The Belgian is expecting to surrender yellow on today’s 108.5km leg from Albertville to the ski station at La Rosiere Espace San Bernardo, a route which closely mirrors stage six of June’s Criterium du Dauphine on which Thomas finished second on his way to overall victory.
“Today was a good day but tomorrow will be super hard,” Van Avermaet said. “I can have a super good day after a rest day but I pay it back…”