"In terms of his GC rivals, it puts the Dutchman 1'20" behind Team Sky's Geraint Thomas, while Adam Yates (Mitchelton-Scott) and Chris Froome are now 21 seconds ahead of the 2017 Giro d'Italia champion.
Dylan Groenewegen (LottoNL-Jumbo) won stage seven of the Tour de France, dominating a bunch sprint after nearly six hours in the saddle.
AG2R's Romain Bardet cracked in the heat of the final ascent and lost 31secs, while fellow contender Tom Dumoulin (Sunweb), the 2017 Giro d'Italia champion, lost almost a minute after suffering a mechanical problem.
Joining Porte in those time gains was Irish stage victor Daniel Martin (UAE), Spaniards Alejandro Valverde (Movistar) and Mikel Landa (Movistar), Briton Adam Yates (Mitchelton-Scott), Welshman Geraint Thomas (Sky), Colombian Nairo Quintana (Movistar), Italian Vincenzo Nibali (Bahrain-Merida), and Dane Jacob Fuglsang (Astana).
"I knew I wouldn't make it back so it was about limiting the time loss", Dumoulin said. "From then on, it was just damage limitation".
Martin was one of several team leaders along with former Tour victor Vincenzo Nibali and two-time runner-up Nairo Quintana who were caught off-guard by an attack by Quick-Step 100 kilometers into the stage during a straightaway that was exposed to crosswinds. Both men could not hold the pace of stage victor Dan Martin (UAE Team Emirates).
Thomas did manage to earn two bonus seconds at an intermediate sprint at Saint-Mayeux, which boosted him to second place overall, just three seconds back on Van Avermaet.
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"Unfortunately didn't get any seconds on the line but yeah there we go", Thomas said. I haven't had the best experience on the Col du Glandon either.
Van Avermaet, a BMC support rider for Porte, kept the yellow jersey for a third straight day.
A group of five riders broke early on the 181km run from Brest to Mur-de-Bretagne and when the Quick Step team of stage contender Julian Alaphilippe suddenly accelerated on the flat, the peloton split into three with 100km remaining.
But it was on the final climb that the action took flight.
As the Australian started to put his foot down, Martin flew past everyone and swiftly opened up a gap with a full 500m to climb.
Having been boxed in the last time the Tour finished on the Mur three years ago, the punchy climber made no mistake this time when jumping off the front of the peloton with 1,200m to go and opening a gap on the highest point of the climb.