Matthews snatches Tour stage 16, Froome in yellow ahead of Alps
The Sunweb Team rider stopped the clock on the 165 kilometer (102.5 miles) leg at 3 hours, 38 minutes and 15 seconds joined by Norwegian Edvald Boasson Hagen (Dimension Data) and Belgian Greg Van Avermaet (BMC Racing).
"It doesn't feel real. We had a goal this morning, it was to try and get the intermediate sprint. Whether it was from the breakaway or trying to somehow distance Kittel, we definitely didn't plan that it would work out like this," the 26-year-old Matthews said.
"I still had full support from three guys. When you have a team riding for you all day and you're sitting out of the wind, what more can you ask for? The spirit in the team is amazing. We're willing to do everything to each other to get a win," he added.
Team Sky's Froome retained the coveted yellow jersey and sits 18 seconds ahead of Italian rival Fabio Aru (Astana) in the overall general classifications with Frenchman Romain Bardet (AG2R La Mondiale) 23 seconds off the lead in third place.
"It's been quite a crazy stage, with a selection being made not long after the climb. A lot of GC guys were quite far up in the peloton. That's why there wasn't much difference between us in the crosswinds. Unfortunately Dan Martin wasn't with us at the end," defending champion Froome said.
"I'm just glad myself and Mikel Landa were on the right side of the split. We have two mountain days ahead of us. I do believe they are the two most decisive consecutive days of the Tour," he added.
The climbers of the pack will be gearing up for Wednesday's stage 17, which will see the race head towards the Alps with a 183 km stretch from La Mure to Serre-Chevalier through three climbs, including two hour category summits.