On Wednesday, Mark Cavendish, Mark Renshaw, Marcel Kittel were all eliminated after failing to make the time cut.
The Isle of Man sprinter, who has amassed an impressive 30 stage wins in 10 previous editions, finished outside the time cut.
Welshman Thomas now leads teammate Froome by 1min 25sec in the overall standings.
Van Avermaet leads Thomas, in second, by 2min 22secs, with Alejandro Valverde now up to third at 3:10.
Andre Greipel and Fernando Gaviria, who finished second and third, were disqualified for being too physical.
The Lotto NL-Jumbo rider beat Quick Step's Gaviria into second place with Slovakian Peter Sagan (Bora) taking third.
Overnight leader Greg van Avermaet finished just three seconds behind in the main peloton to retain the yellow jersey.
Overnight leader and Olympic road race champion Greg van Avermaet (BMC) retained the yellow jersey.
Colombian Gaviria won Saturday's first stage on his Tour debut and looks to be the man to beat in the sprints this year.
Belgian team Quick Step came third at seven seconds.
Overnight leader Fernando Gaviria came down in a mass high-speed crash just 1.3km from the line.
Colombian Nairo Quintana also lost valuable seconds after suffering a puncture close to the finish.
Roadside fans are urged not to verbally abuse Kenyan-born Briton Chris Froome following a slanderous saga surrounding a leaked doping suspicion.
Four-time champion Froome was cleared of doping suspicions by UCI, headed by David Lappartient.
Tour de France organisers had on Sunday banned Froome from taking part to protect the integrity of the world's best-known cycling race.