The judges needed the photo, but it wasn't that close in the end with the Canberran clearly ahead of unlucky again Edvald Boasson Hagen (Dimension Data) and John Degenkolb (Trek-Segafredo).
Kittel was gapped on the opening climb and ultimately finished the stage, 16 minutes and 19 seconds down. As a result, the German was unable to contest the intermediate and final sprints which Matthews plundered.
"I still cannot believe it," Matthews said. "We went in to today hoping QuickStep would let me go in the breakaway and take the intermediate but then you got a gamble on the finish whether you still got legs to sprint. Somehow we ended up with both."
"We had a pretty open plan this morning. We had no idea what was going to happen. It was an eight-man team time trial to the finish.
"I'm just so thankful for this opportunity from Team Sunweb to give these great guys, to support me in the biggest race of the year, to be able to finish it off for them is even more special."
Bling took advantage of Sunweb's hard graft from the flag drop, which according to the data, amounted to 69.1 per cent of the work done by the peloton.
While Thomas De Gendt (Lotto Soudal), Sylvain Chavanel (Direct Energie) Daryl Impey (Orica Scott), Nicholas Edet (Cofidis) and Thomas Degand (Wanty) went ahead on the first climb, Matthews kept in touch by his own counter attack as he tried to bridge to team mate Simon Geschke sitting between the leaders and the peloton.
This attack was foiled by Dan Martin (QuickStep Floors) who knew Sky would work if he went off the front himself to help team mate Kittel. But that's when QuickStep's luck ran out as Sunweb caused a split in the peloton on the climb and the German was spat out the back, quickly losing 50 seconds.
After the leaders crested Boussoulet first, it was soon all together again. The peloton remained the 'breakaway' until the crosswinds caused tension and a split in the final 16 kilometres.
Matthews was again in the right position as were GC favourites Christopher Froome (Sky), Rigoberto Uran (Cannondale Drapac) and Fabio Aru (Astana). Romain Bardet (Ag2R) almost missed the split but was ably hooked back on by Oliver Naesen's hard work.
But wafer thin Dan Martin fared poorly, missing out despite hiding behind hard as nails team mate Jack Bauer. The Irishman struggled so much, at one point he detached from the New Zealander and finished 51 seconds behind. He now slips to seventh overall, two minutes and three seconds behind race leader Froome.
More to come