Yates lost touch from the back of the favourites group on the Col des Glieres and rode his momentum to the top and over the gravel section.
Teammate Esteban Chaves re-joined Yates and worked to drive his team leader down the valley to limit the damage.
With a lumpy stage tomorrow and penultimate-day time trial before the traditional Champs Elysees stage in Paris, Yates sits in seventh overall, five-minutes 55seconds behind race leader Roglič .
"In the beginning it was fine, everything was under control and I had a lot of teammates around me and we just tried to stay cool and out of trouble," said Yates. "As the day went on it just got worse and worse, it is stage 18 of the Tour so I think everybody is tired and so am I.
"We held on for as long as we could but in the end, we lost some time but I am still inside the top 10 on GC."
The Col des Glieres proved to be too much for Yates, who held the yellow jersey for four stages earlier in the race after a penalty was applied to Julian Alaphilippe (Deceuninck-QuickStep) for accepting a late bidon on Stage 5. Yates kept the jersey until the conclusion of Stage 9 when Primož Roglič took over the race lead.
“It was a really tough climb, we’ve done it before in the Tour in 2018, so I knew it was going to be really tough, especially with the gravel section over the top," said Yates of the climb. “Once I started suffering, I just tried to keep calm and tried to pace myself a little bit and then took a bit of a rest of the descent. Thankfully I had Esteban with me, we worked well in the valley towards the finish but again it was a hard day.
“It was tough [the gravel section] and there were quite a lot of holes, by that point I was still off the back and trying to find my rhythm and trying to pace myself and then once we got over the top I was with Esteban and we did what we could to get back, but unfortunately today wasn’t enough.”
Yates is a minute and 36 seconds behind Enric Mas (Deceuninck-QuickStep) sixth place, but will likely face pressure from Rigoberto Uran (EF Education First) and Tom Dumoulin (Jumbo-Visma) in the time trial as the lower placed rivals on the general classification are both well within striking distance.
The 2020 Tour de France continues with the 166km Stage 19 from Bourg-en-Bresse to Champagnole that could decide the green jersey. Watch on SBS HD and SBS On Demand from 9:30pm AEST and the SBS ŠKODA Tour Tracker from 9:20pm AEST.