Kelderman did make the front group after the crash that came with 26km to go. But the Sunweb rider stopped by the side of the road around seven kilometres later with a mechanical and more crosswinds still to face.
Starting their frantic chase as the fourth group on the road and at one minute and 27 seconds down, the Dutchman and his Sunweb soldiers hooked on to Pinot's group with eight kilometres to go.
Thibaut and Pinot finished the stage one minute and 44 seconds behind the main bunch.
“It was already a really hectic stage because of the side-tailwind," Kelderman said, now two minutes and 50 seconds in deficit to race leader Rudy Molard. "We went into a village and there was a crash in front of me and Mike (Teunissen). I managed to brake but Mike unfortunately crashed.
"I carried on riding but my back wheel was really rubbing on my brakes. Initially I was still there but the bunch went full gas and after the bike change I had already lost a minute or so.
"The team did an awesome job but of course I’m really disappointed. Luckily I didn’t crash and still have good legs. The Vuelta is not over yet so we will see what happens in the upcoming days.”
Pinot's Groupama-FDJ director Franck Pineau said all is not lost despite Pinot now three minutes and eight seconds down on GC.
"This is not a catastrophe, the mountains remain to come. You have to bounce, nothing is finished, the road is still very long. Pinot remains our undisputed and undeniable leader."
Pinot's team mate and race leader Rudy Molard managed to miss out on all the action, somehow finding himself in the front group.
"I was at the front at this moment," he said. "I was fighting to keep my body in the first position. It was a very hard fight with the team. I don't know what happened with Thibaut. I'm very disappointed for Thibaut today."
How the GC looks now after Stage 6's shenanigans:
Apart from Pinot and Kelderman, all the other main contenders made the front group.
Bora-hansgrohe successfully defended Emanuel Buchman's GC position, safely ensconcing he and Peter Sagan in the front group but Rafal Majka suffered in the process, finishing the stage over three minutes down. He has now slipped out of the top 20, and is four minutes and 28 seconds in deficit to Molard.
The top 15:
1. Rudy Molard (Groupama-FDJ)
2. Michal Kwiatkowski (Sky) + 41
3. Emanuel Buchmann (Bora-hansgrohe) +48
4. Simon Yates (Mitchelton-Scott) +51
5. Alejandro Valverde (Movistar) +53
6. Ion Izagirre (Bahrain Merida) +1.11
7. Tony Gallopin (AG2R Mondiale) +1.14
8. Nairo Quintana (Movistar) +1.14
9. Steven Kruijswijk (LottoNL Jumbo) +1.18
10. Enric Mas (Quick-Step Floors) +1.23
11. George Bennett (LottoNL Jumbo) +1.26
12. Miguel Angel Lopez (Astana) +1.27
13. Fabio Aru (UAE) +1.28
14. Rigoberto Uran (EF Drapac) +1.29
15. David De La Cruz (Sky) +1.34