The new race leader has an advantage of 1 minute 25 seconds over Froome, who moves to second overall, with Dumoulin a further 19 seconds back in third place. "It's a bonus for me to be up there, and hopefully I can be there for as long as possible".
After his Australian BMC teammate Richie Porte crashed out of the Tour on Sunday, Van Avermaet started the second week with no agenda but to stay in yellow as long as he could, and put in a ride to honour the jersey.
The 109-mile stage features three beyond-category climbs - Col de la Madeleine, Croix-de-Fer and the iconic Alpe d'Huez finish after 21 switchbacks to close out the Tour's three days in the Alps. He is now 20 minutes behind Thomas.
Van Avermaet is a super one-day racer but not a strong climber.
Team Sky's Geraint Thomas attacked in the finale of the 11th stage as 2017 Giro champion Tom Dumoulin took second place.
"This is where it gets hard, as we hit first mountain stage", said the former Sky leader on Eurosport's The Bradley Wiggins Show. "I didn't expect it at all".More news: Twitter chief Jack Dorsey caught up in purge of fake followers
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.
Yet Thomas, a former track cycling Olympic champion like 2012 Tour victor Bradley Wiggins, has yet to prove he can handle the pressure of a grand tour. I knew it was a good chance but I didn't know what everyone else would ride like.
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The Belgian rider was joined in the lead by fellow General Classification contender Philippe Gilbert and green jersey leader Peter Sagan but Team Sky riders Geraint Thomas and Chris Froome remained behind.
But Thomas and Sky have played that down. For me it's an unknown.